{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quadrature\n",
    "\n",
    "This is a notebook that illustrates differences in the quadrature methods which are central to the evaluation of\n",
    "\n",
    "$$\n",
    "\\int_0^{\\pi} f(\\theta) \\sin \\theta \\; \\mathrm{d}\\theta = \\int_{-1}^{1} f(\\cos \\theta) \\; \\mathrm{d}\\cos \\theta.\n",
    "$$\n",
    "\n",
    "Quadrature is used to compute the projection onto the associated Legendre functions in `paddle-harmonics`.\n",
    "\n",
    "In order to illustrate how interpolation and quadrature affect the error in the computation of the SHT, this notebook contains example for both errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import paddle\n",
    "import scipy\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_theta = 80"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(\"../paddle_harmonics\")\n",
    "\n",
    "from quadrature import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test interpolation\n",
    "\n",
    "we first assess the interpolation onto the quadrature nodes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# interpolation - careful - this breaks if points align (for non-periodic signals)\n",
    "def interpolate(t, tq, f):\n",
    "    j = np.searchsorted(t, tq) - 1\n",
    "    d = paddle.to_tensor( (tq - t[j]) / np.diff(t)[j] )\n",
    "    j = paddle.to_tensor(j)\n",
    "    interp = paddle.lerp(paddle.to_tensor(f[j]), paddle.to_tensor(f[j+1]), d)\n",
    "    # interp = f[j] + (f[j+1] - f[j]) * (tq - t[j]) / np.diff(t)[j]\n",
    "    # print(d)\n",
    "    # print(f[j+1] - f[j])\n",
    "    # print(j)\n",
    "    return interp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "cost_lg, wlg = legendre_gauss_weights(n_theta, -1, 1)\n",
    "# cost_lg, wlg = lobatto_weights(n_theta, -1, 1)\n",
    "tq = np.flip(np.arccos(cost_lg))\n",
    "teq = np.linspace(0, np.pi, n_theta, dtype=np.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(teq, '.')\n",
    "plt.plot(tq, '.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "test interpolation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "W1106 16:08:59.919569 66890 gpu_resources.cc:119] Please NOTE: device: 0, GPU Compute Capability: 7.5, Driver API Version: 12.3, Runtime API Version: 12.4\n",
      "W1106 16:08:59.920946 66890 gpu_resources.cc:164] device: 0, cuDNN Version: 9.4.\n"
     ]
    }
   ],
   "source": [
    "f = lambda t : np.cos(4*t)\n",
    "# f = lambda t : 1 / (1 + 25 * (2*(t-np.pi/2)/np.pi)**2)\n",
    "# f = lambda t : 1 / (1 + 25 * np.cos(t)**2)\n",
    "# f = lambda t : t**5 - 3*t**2 - 2*t + 1.0\n",
    "\n",
    "interp = interpolate(teq, tq, f(teq))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Tensor(shape=[80], dtype=float64, place=Place(gpu:0), stop_gradient=True,\n",
       "       [0.99051621, 0.96017247, 0.90654557, 0.83090023, 0.73507102, 0.62138695,\n",
       "        0.49261122, 0.35187340, 0.20259315, 0.04839723, -0.10696858, -0.25973031,\n",
       "        -0.40617737, -0.54275253, -0.66613820, -0.77333689, -0.86174389, -0.92921053,\n",
       "        -0.97409622, -0.99530837, -0.99232890, -0.96522689, -0.91465698, -0.84184357,\n",
       "        -0.74855128, -0.63704220, -0.51002113, -0.37057012, -0.22207379, -0.06813728,\n",
       "        0.08750110, 0.24106052, 0.38880936, 0.52715572, 0.65273465, 0.76248985,\n",
       "        0.85374796, 0.92428359, 0.97237355, 0.99683884, 0.99683884, 0.97237355,\n",
       "        0.92428359, 0.85374796, 0.76248985, 0.65273465, 0.52715572, 0.38880936,\n",
       "        0.24106052, 0.08750110, -0.06813728, -0.22207379, -0.37057012, -0.51002113,\n",
       "        -0.63704220, -0.74855128, -0.84184357, -0.91465698, -0.96522689, -0.99232890,\n",
       "        -0.99530837, -0.97409622, -0.92921053, -0.86174389, -0.77333689, -0.66613820,\n",
       "        -0.54275253, -0.40617737, -0.25973031, -0.10696858, 0.04839723, 0.20259315,\n",
       "        0.35187340, 0.49261122, 0.62138695, 0.73507102, 0.83090023, 0.90654557,\n",
       "        0.96017247, 0.99051621])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.98737534,  0.94982013,  0.88828261,  0.80431657,\n",
       "        0.70004207,  0.578092  ,  0.4415455 ,  0.29385027,  0.13873553,\n",
       "       -0.01988219, -0.1779979 , -0.33161928, -0.4768675 , -0.61007515,\n",
       "       -0.72787881, -0.82730403, -0.90584039, -0.9615049 , -0.99289207,\n",
       "       -0.9992094 , -0.98029737, -0.9366335 , -0.86932027, -0.78005731,\n",
       "       -0.67109843, -0.54519477, -0.40552532, -0.25561663, -0.0992538 ,\n",
       "        0.05961513,  0.21697881,  0.36886392,  0.51143548,  0.64109364,\n",
       "        0.75456462,  0.84898336,  0.92196585,  0.97166934,  0.99683884,\n",
       "        0.99683884,  0.97166934,  0.92196585,  0.84898336,  0.75456462,\n",
       "        0.64109364,  0.51143548,  0.36886392,  0.21697881,  0.05961513,\n",
       "       -0.0992538 , -0.25561663, -0.40552532, -0.54519477, -0.67109843,\n",
       "       -0.78005731, -0.86932027, -0.9366335 , -0.98029737, -0.9992094 ,\n",
       "       -0.99289207, -0.9615049 , -0.90584039, -0.82730403, -0.72787881,\n",
       "       -0.61007515, -0.4768675 , -0.33161928, -0.1779979 , -0.01988219,\n",
       "        0.13873553,  0.29385027,  0.4415455 ,  0.578092  ,  0.70004207,\n",
       "        0.80431657,  0.88828261,  0.94982013,  0.98737534,  1.        ])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(teq)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plt.plot(teq, f(teq), '.-', label=\"reference\")\n",
    "plt.plot(tq, f(tq), '.-', label=\"reference\")\n",
    "# plt.plot(tq, interp, '.-', label=\"interpolated\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test quadrature with associated Legendre polynomials\n",
    "\n",
    "let us test different quadrature modes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def precompute_legpoly(m_max, l_max, x):\n",
    "    \"\"\"\n",
    "    Computes the values of P^m_n(\\cos \\theta) at the positions specified by x (theta)\n",
    "    The resulting tensor has shape (m_max, l_max, len(x))\n",
    "    \"\"\"\n",
    "\n",
    "    # compute the tensor P^m_n:\n",
    "    pct = np.zeros((m_max, l_max, len(x)), dtype=np.float64)\n",
    "\n",
    "    sinx = np.sin(x)\n",
    "    cosx = np.cos(x)\n",
    "\n",
    "    a = lambda m, l: np.sqrt((4*l**2 - 1) / (l**2 - m**2))\n",
    "    b = lambda m, l: -1 * np.sqrt((2*l+1)/(2*l-3)) * np.sqrt(((l-1)**2 - m**2)/(l**2 - m**2))\n",
    "\n",
    "    # start by populating the diagonal and the second higher diagonal\n",
    "    amm = np.sqrt( 1. / (4 * np.pi) )\n",
    "    pct[0,0,:] = amm\n",
    "    pct[0,1,:] = a(0, 1) * cosx * amm\n",
    "    for m in range(1, min(m_max, l_max)):\n",
    "        pct[m,m,:] = -1*np.sqrt( (2*m+1) / (2*m) ) * pct[m-1,m-1,:] * sinx\n",
    "        if m + 1 < l_max:\n",
    "            pct[m,m+1,:] = a(m, m+1) * cosx * pct[m,m,:]\n",
    "\n",
    "    # fill the remaining values on the upper triangle\n",
    "    for m in range(0, m_max):\n",
    "        for l in range(m+2, l_max):\n",
    "            pct[m,l,:] = a(m,l) * cosx * pct[m,l-1,:] + b(m,l) * pct[m,l-2,:]\n",
    "\n",
    "    return paddle.to_tensor(pct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us plot the Legendre polynomials:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_66890/718935433.py:9: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown\n",
      "  fig.show()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = 0\n",
    "\n",
    "pct = np.sqrt(2 * np.pi) * precompute_legpoly(n_theta, n_theta, teq)\n",
    "pct = pct.numpy()\n",
    "\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "for l in range(6):\n",
    "    ax.plot(np.cos(teq), pct[0, l])\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def project(t, w, f, mmax=None):\n",
    "    m = 0\n",
    "    if mmax == None:\n",
    "        mmax = len(t)\n",
    "\n",
    "    weights = paddle.to_tensor(w)\n",
    "    pct = np.sqrt(2 * np.pi) * precompute_legpoly(mmax, mmax, t)\n",
    "    weights = paddle.einsum('mlk,k->mlk', pct, weights)\n",
    "\n",
    "    proj = paddle.einsum('...k,lk->...l', paddle.to_tensor(f), weights[m])\n",
    "    rec = paddle.einsum('...l, lk->...k', proj, pct[m] )\n",
    "    return rec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let us compare the accuracy of the different projection methods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0, np.pi, n_theta)\n",
    "plt.plot(t, f(t), label=\"reference\")\n",
    "\n",
    "for quadrature in [legendre_gauss_weights, lobatto_weights, clenshaw_curtiss_weights, fejer2_weights]:\n",
    "    cost, wq = quadrature(n_theta, -1, 1)\n",
    "    tq = np.flip(np.arccos(cost))\n",
    "\n",
    "    out = project(tq, wq, f(tq)).numpy()\n",
    "\n",
    "    plt.plot(tq, out, '.-', label=quadrature.__name__)\n",
    "\n",
    "plt.legend(loc='lower left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for quadrature in [legendre_gauss_weights, lobatto_weights, clenshaw_curtiss_weights]:\n",
    "    cost, wq = quadrature(n_theta, -1, 1)\n",
    "    tq = np.flip(np.arccos(cost))\n",
    "\n",
    "    out = project(tq, wq, f(tq))\n",
    "    # print(np.abs(out - f(tq)))\n",
    "\n",
    "    plt.semilogy(tq, (out - f(tq)).numpy(), '.-', label=quadrature.__name__)\n",
    "\n",
    "plt.legend(loc='lower left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now add interpolation into the mix to evaluate performance with interpolation taken into account. For this particular case, we will assume that the data is given to us on an equidistant grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EJ0RriQuMY9QGbeapZX0NGAxGMoZkuP1xRxIcFzQ2fSz/97cF5EVDgBX85y/VOyQhWl3e5kxMPwc6dkIKkLAqgLzNmXqG5ZC3OZO4I8d6XRpUiP/ZdeITorWs+PRNkg6r1PjARePuYel1SxmbPlbvsM6aJDguKjmmM/l9YwGI/XUL9qzl8stReJT8whIMTdSAMheW6BLPifILSxrtIF0pPiFaS+kX7wCwq7ORqy661+1bbo6SBMeF9b/rcWp8IP6wysFXb4RZPaQPgPAYCX0u5oT8BpsCpj4X6xLPiRL6XNxo2KwrxSdEayj59gXa76oGwNShxKOOMZLguLBu7bqwu7M2aDxrXyioUoRTeI6I+DRqfI9dtylQMOlaEjv01C+o4yR26Il50rXYjkty9lw70GXiE+KsWXLZ8enr+NogJw7ODS7zqGOMJDiurCiLyI4VAETt9cVao4CbFj0T4kTfvfkoAVYoDQTLM38n6uvPGX6vfhP8NWX4vU8T9fXn5MRr16sPHdQ3ICFakf3wbuy7tEktLV1r8VPwqGOMJDiuLKojQ0MqyI4DvzrYui0Ca5WvWxY9E+JE6srlABzoFsS5197tsi0jiR16UjIkHYCELflSn0p4jLWLfiSyWKHaB/olWLSFblpYsymS4Liy8CSCRr+CGlEHgP/OQPYsiqNk2WqdAxPi7JgPZtEhqxaA6MvH6BtMM1zwt6ep9oW4Ylj+2Wt6hyPEWSuZP5+wtz4HwL9OJXqvr5bcuGlhzaZIguPirImXkbr7uI4KqioVxoXbWzF7Gn51YI6CYTc/rHc4p5WQ1oN9HX0AOLL4Y52jEeLsHK0cfrR7mYJC/voorDf/4LaFNZsiCY6Lq91/AEU9YayJVBgXbi7kN62ArLlHNEYf39Os7RoM550LQLudZVRWlOkcjRBnrqnK4djt1BbX6hOQk0iC4+L80trBCYUHVYMBS2ygThEJcXa2rv2etBxt59r15vt0jqb5Lvvrs5QGQVglfPfWo3qHI8QZs8QFNZqiAYMBv3apeoTjNJLguDhfk4mEmTMaJDmLB6hc/vOtLNi9QMfIhDgzf3zwLAZgf5JC34tv1DucZgsKi+ZAlyAA1BXL9Q1GiDO0YPcCblhyS8MEx2AgYeYMt64c3hRJcNxAxLhxhH/1Kes7atcDrGBX7cxYPQNzhfTFEe4lbrM2x0Zpn/Y6R9JykfUdottn1VJwMEvfYIRoIXOFmRmrZzBgl037kRELM2/xIfyrT4kYN07v8FqdJDhu4mBgFUsGaG/XoF0qil3FrtrJKcvROTIhmu/nT54j8RBYjTDkrif0DqfFLvnTNAojwb8OfnnlXo+ZEE14h+zSbOyqncE7tfabVecY2JIKuUHVOkfmHG2S4MyePZu0tDQCAgIYPHgwa9euPem6w4YNQ1GURpcrr7zSsc5tt93W6PZRo0a1xaboJjUslW3tDJQHQEQFdMkFg2Jw+3L2wotsmMfhRVrNmwNpdlIrtugcUMsZfXw43FXr/+a/aR9r3+yPec1snaMSonlSw1IJqVLocUBLcNZ0UTz6OOL0BOezzz5jypQpZGRksGHDBnr37s3IkSMpLCxscv0FCxaQn5/vuGzZsgWj0cj111/fYL1Ro0Y1WO+TTz5x9qboyhRs4tELZvBbJ21g37nb7R5Rzl54CUsuCxc/gmmHNmLqf718WPDjI+7XAmLJpX+8Nptxu2wDbxdHc/Oaf7Ng03s6BybE6ZmCTdy0PxkfO+yPg8Joo0cfR5ye4Lz88stMnDiRCRMm0L17d958802CgoJ4//33m1w/KioKk8nkuCxbtoygoKBGCY6/v3+D9SIjI529Kbobmz6WsF5dARiyS+XqtKt1jkiI5jkw7w3SPwklvApUILRSZUZ0BOb89XqH1jJFWQQE15Efoe08H1ho5/U37Kyc+3/SH064hQ6btAQ9Pz2IpdctZWz6WJ0jch6nJji1tbWsX7+eESNGHHtCg4ERI0awenXzZuN97733uOmmmwgODm6wfPny5cTFxdGlSxfuvvtujhw5ctLHqKmpobS0tMHFXY28/Rmq/CCyDH764g29wxHitKxmMxX/XuDY2SjAHd+pRJRBjo+PnqG1XFRHcqz+xJccW2RQ4c5vbRzM2qRbWEI0x6HcHNplWwHocNk4j225OcqpCc7hw4ex2WzEx8c3WB4fH4+5GTPxrl27li1btnDnnXc2WD5q1CjmzZtHZmYmzz33HCtWrODyyy8/aY2YZ555hvDwcMclJcV9zzfGJHdhb3sjAJav57pfE7/wOk1NVmlUIbEYUhL66RTVGQpPwtThtkY7TqMK8cWNZhYRwqX8+saD+Nq0GcTPHztF73CczqVHUb333nv07NmTQYMGNVh+0003cfXVV9OzZ0/GjBnDV199xbp161i+fHmTjzNt2jQsFovjkpPj3iOPDN1iAYjbXY79/3rAhnk6RyTEyfmltUNVlAbLbArcfOkDbvkL0jTq/kbboxoUTF366BOQEM2xYR4BG7RTwsXtrfhs/kzngJzPqQlOTEwMRqORgoKCBssLCgownWZCoYqKCj799FPuuOOO0z5Phw4diImJYc+ePU3e7u/vT1hYWIOL27LkcoH/H1T7QmSpQp7FFxZPlpYc4bJ8TSYOdghxXFcNBkIfncrVQyboGNWZ8zWZSHxipmOiNBVInDnT4yZJEx7EkkvtgsnEZWut/0mJlV5x3HBqguPn50f//v3JzMx0LLPb7WRmZjJkyJBT3veLL76gpqaGW2+99bTPc/DgQY4cOUJCQsJZx+zyirKIVerY306b6n53fgioNijaq3NgQpycsbQcgL3nJZH+Qybtbjn9DxdXFjFuHIf/oU2MZjWCOuwinSMS4hSKsth+KBC/OiiMgL5BFV5x3HD6KaopU6bwzjvvMHfuXLZv387dd99NRUUFEyZov97Gjx/PtGnTGt3vvffeY8yYMURHRzdYXl5ezj//+U9+/fVX9u/fT2ZmJtdccw2dOnVi5MiRzt4c/UV1BMWAT2oNAH77/bBjhKgOOgcmRNO2/racxEMqdiD93oc8pqXjvNsf5UgY+Nlgxdwn9Q5HiJOL6sihXK3MSGGHOvwUQPH844bThzDceOONHDp0iOnTp2M2m+nTpw9LlixxdDzOzs7GcEIxyZ07d/Lzzz/z3XffNXo8o9HIH3/8wdy5cykpKSExMZHLLruMJ554An9/f2dvjv7Ck2D0K/T63wOUGAOJKlHYk3IHncOT9I5MiCZt/mQWvYGcRBjV71K9w2k1Rl9/8toHEL2pGuuaVXqHI8RJVRBGzAHtcB+bVKklN6NnaccTD9YmYzQnTZrEpEmTmrytqY7BXbp0QVWbHpEQGBjI0qVLWzM899NvPO06Due3dSPovhf2fruO9leaPeaXsfAsQdu0mk0lnWJ0jqT1+Q0YCJt+InlvBba6OozuNuxdeIVfXp1JshWKgmHA7W9BYl+PT27AxUdRiVMITyIgNByAdlsK2HPJcErmz9c5KCEaKjqUT7ucOgCSLvW8CcUu+sujVPtCRDms/PItvcMRopGS+fNJ+ugrACIroG5rtVckNyAJjtuyms20/+O4CQvtdvKnZ2BtxvxCQrSV5e8/gV8dHAmDodc23YrrziLjUslO1UamFCz9XOdohGjIajaTPz2Do5MaKOBVxwlJcNxUU5OnYbdTeyBbn4CEaIL9t18ByOsQiNHHV+donKP6nPYARO8+pHMkQjRUu/8A2O0NF3rRcUISHDfll9YOTuicjcGAX7tUfQIS4gR1tVaS9lYB4D/o1NNCuLM+N94PQHKByvYNK3SORohj/NLa0ag3qxcdJyTBcVO+JhMJM2eg1rc9qsC7lyosLvtF17iEOGrlf2cTUQFVfjDstn/pHY7TdOk/gpz6/v1/fDpL11iEON7isl84fNy8tqpBIWHmDK8ZkCIJjhurvvx87r3bh9KA+nOrkSozVs+QqsbCJRR+/18AslONhEcl6hyNcxWlayPEArc0PZu6EG3NXGHm5WUZxNZ31XzhWgP33uND9eXn6xtYG5IEx41ll2ZzOBzWd9aacfrsVbGrdnLK3LvWlvAMMbsPA1DTo5POkTifaYQ2Qiw1u46Sw/k6RyOEdnzouU/rf7MvHtZ1NXA4VPWq44MkOG4sNSwVg2JgY3stwem9T8WgGEgJdd9q6cIzbF/+GUmFYAf63uz5VYsvuO4+ikLBvw5+eXOyx9f4Ea4vNSyVPnu1Hjib6o8R3nZ8kATHjZmCTWQMyWBrmhE7kHoI7ou7xS0rNAsPsmEeWR89DEBugkpn235942kDRh8fCtK0Sf4qNv2O+bXesGGezlEJbxbjF0PvffUJTgcFg2IgY0iGVx0fJMFxc2PTx/LfPy8lu77OaNiK3/UNSHg3Sy4LfpxGeU4AAOtTFRb8+Ijnt2hYcilJrQAgZY+Rm0PjvGO7hctatXge4ZVQ7Qt3j3uWpdctZWy65022eSqS4HgAU0gCljStq7zf1u06RyO8mTn/N1YdCKfXfu361Wth5cEwzPnrdY3L2cz5v7G1LgAVCK+C199UvWK7hevKX/YpANkpBi7qPtqrWm6OkgTHQ4SdeyEAydk1WGtqdY5GeKuckgpu/051zJxqUOHOJSoHS8p1jcvZvHW7heuK2K21HlakJ+gciX4kwfEQF970Tyr8Ibga1r33T2kaF7owVUc22qkYVYividIlnrZiqo7EcMKMat6w3cI1Hdm9jqQ8bQRVu5E36ByNfiTB8RAh4XHkpGq/HytWLYZZPaSTo2hzpq59G82cqhoUTF366BFOmzF17YuqKA2WecN2Cxe0YR77/+9afOxQGAFD4/z0jkg3kuB4Cksu/gnatPiGPF9Q7bB4srTkiDaVXZxPg8O8wUDizJkeP3Oqr8lE4hMzG5RPKbyot8dvt3AxllxYfD+HC7RO/kUpNpSvp3jtcUASHE9RlEWnGG0Uh8lsoNKqgGqDor06Bya8yYbPXwXAHAWpc+fS6YdMIsaN0zmqthExbhydfshkf1p9dfEK7yhoKFxIURaodkIOalMWhJmqvPo4IAmOp4jqSLq/lfxorYPj9iMhoBghqoPekQkvomz5A4DC9sEEDx7kdS0YviYTZf3SAYg6UKxzNMLrRHWksNKfKItCnQF6RFZ49XFAEhxPEZ6EMvoVipPrADhiDoTRsyA8Sd+4hFeJz64EwK93H30D0VHPq24HILFAJSdrq87RCK8SnsRvFV0AyE5SiTfi1ccBSXA8Sb/xqH0HABB60Ad7n1t1Dkh4k40/fUOMBeoMMOSGyXqHo5tuQ67CHKXtXNd99ore4Qgvo+61AGBJC4HJm6HfeJ0j0o8kOB7m3JsfotYHIsph85uvYTVLZXHRNnYufg+AgwkKprQeOkejI0XhULtAAGybZGZx0XbK9+4nOdsKQPh5l3pty81RkuB4mOR2fSjSJjXG79U32XPJcErmz9c3KOEV/HbuAcDSLlznSPTn00NL8OKyZaI/0TZK5s8n+8or8LOBCvT36ax3SLqTBMfDWM1m4ouOW2C3kz89Q1pyhFPZ6upIzNFm0A4beL7O0ehv4PX3Y1cgrhi2/bZc73CEh7OazeRPz0BRtVmoFKD46Re9fr8vCY6Hqd1/oOE8JAB2O7UHZMiqcJ5fvppDWCXU+ML5Nz2gdzi6S+ncn9x47f8tC97QNxjh8Wr3HwC7veFC2e9LguNp/NLaNZhsDACDAb92qfoEJLxCbqZ2GjQnyUBYpHcNDT+ZonbauWLj9p06RyI8nez3myYJjofxNZlImDnDMV2+CgT9a4rXzUci2lbwHm2m1PIOcTpH4jqC+p8LQGJODba6Op2jEZ7M12Qi57zuxxYYDCTMnOH1+31JcDxQxLhx/HxhKAA7kuFq26ss2L1A56iEp6osLyUp1wZA/PlX6ByN67jgxgeoNWojGtcu+1TvcIQHW7B7ARtrtDmX1neE3e9N9ZoZxE9FEhwPZK4w82UXrS5VBzModTZmrJ6BucK7O5wJ5/jpi1cIrIWyQDh/7CS9w3EZkfGpHEzUesQd+O4TnaMRnspcYWbG6hl0y9ba7Vd1N/DY7lmyv0cSHI+UXZrNwWgVSxD410GnfLCrdnLKcvQOTXig4lXLAMhN9sEvIFDnaFxLafsYAAJ3e3dnT+E82aXZ+FfZ6FCgXd+Wqsj+vp4kOB4oNSwVg8HItlTt12P3AyoGxUBKaIrOkQlPFL7/MADWjgk6R+J6oodeCkBSTh01O5Z5bVVn4TypYal0O6jVIMyPhKIwRfb39STB8UCmYBMZQzIcCc452SoZQzIwBXt3hzPR+op/mEVSvtY03t9vE2yYp3NEruWC6++n0g+Ca2DP23+GWT3kNRKtyhRs4vwDAYDWemNQDLK/rycJjocamz6WS4beBECXXJWRCZfqHJHwOJZcfv/fS/jaoCgU2gdWw+LJ0kpxnMC6MgqStPlJthSHYDYo8hqJVtfuQH2R2/bJLL1uKWPTx+ockWtokwRn9uzZpKWlERAQwODBg1m7du1J1/3ggw9QFKXBJSAgoME6qqoyffp0EhISCAwMZMSIEezevdvZm+F2Lhv7AGWB4G+Fn/87W+9whIdZsPU//FEQAsCOJFgYGgyqDYr26hyZCynKoiBFG2EWtNeXm8MTWBAcIK+RaDXm3P0kFWqtqIMvv0Nabo7j9ATns88+Y8qUKWRkZLBhwwZ69+7NyJEjKSwsPOl9wsLCyM/Pd1wOHDjQ4Pbnn3+eV199lTfffJM1a9YQHBzMyJEjqa6udvbmuBUfvyDykowAFP+yTOdohCcxV5hZOf9DLtuoXT93B6zMjcDs4wtRHXSNzZWYA8M4YPcDoFMBvP6GXXudAkN1jkx4ijWfv4pBhUPh0OuC6/UOx6U4PcF5+eWXmThxIhMmTKB79+68+eabBAUF8f7775/0PoqiYDKZHJf4+HjHbaqqMmvWLB599FGuueYaevXqxbx588jLy2PhwoXO3hy3U9VB6/gZur9A50iEJ8nJ2sjEb22OsiAG4M4lKgd73uX1FYyPl1No5vpVquO6Qa1/nQrl+yhaR83vvwJQkOyHcuJsxl7Oqa9GbW0t69evZ8SIEcee0GBgxIgRrF69+qT3Ky8vp127dqSkpHDNNdewdetWx2379u3DbDY3eMzw8HAGDx58ysf0VqYLtInXkvJsVJllynjROkxFKga14TKjCvERF+oTkIs66etUrDZ9ByFaKDK7BAB7p2R9A3FBTk1wDh8+jM1ma9ACAxAfH4/5JFVOu3Tpwvvvv8///vc/PvzwQ+x2O0OHDuXgwYMAjvu15DFramooLS1tcPEWQ1PCHP1w9j83TEZwiFZh6tqXEw/RqkHB1KWPHuG4LFPXvqhKw/K38jqJ1lL8/f+RUKB9Ewcaf5P9+wlcrj1ryJAhjB8/nj59+nDRRRexYMECYmNjeeutt874MZ955hnCw8Mdl5QUL5kfwJKL/9KpFCRqozhyDwfKCA7RKnxNJorCj1tgMJA4c6bX1745ka/JROITMx1JjgrEPvqovE7i7Fly2bfwJYwqHA6H9n4yivFETk1wYmJiMBqNFBQ0PN9cUFCAqZlfcF9fX/r27cuePXsAHPdryWNOmzYNi8XiuOTkeMkMj0VZoNoxxFsBsBf4yigX0SosRYcIL9P+r7z3Jjr9kCm1b04iYtw4Ur/+H9W+oABbjEV6hyQ8QVEWhw77a/8m1veHk/17A05NcPz8/Ojfvz+ZmZmOZXa7nczMTIYMGdKsx7DZbGzevJmEBK2zbPv27TGZTA0es7S0lDVr1pz0Mf39/QkLC2tw8QpRHUExkBytzZEQm2/AphpllIs4a6vmz8bHDiXB0OfuR6RF4jRCOqRzMFnb3Ras+lrnaIRHiOqIj9kHgIC4Wm2ZIvv34zn9FNWUKVN45513mDt3Ltu3b+fuu++moqKCCRMmADB+/HimTZvmWH/mzJl899137N27lw0bNnDrrbdy4MAB7rzzTkAbYTV58mSefPJJFi1axObNmxk/fjyJiYmMGTPG2ZvjXsKTYPQrdA2upTwAAqzwW8Q1MspFnLXS31YAYE7ywejjq3M07qE8NRqAgL1yCkGcveJqA/EF2iG8Q1SlltyMniX79+P4OPsJbrzxRg4dOsT06dMxm8306dOHJUuWODoJZ2dnYzhuaFtxcTETJ07EbDYTGRlJ//79+eWXX+jevbtjnQcffJCKigruuusuSkpKOP/881myZEmjCQEF0G88/h2Hk7vuUrpkqRzYlctgvWMSbi/kwCEAatKk5aa5IvsPhRX/IyHPis1mw2g06h2ScGO/fvYqafX9b86b+DlEp0tycwJFVVWvG69YWlpKeHg4FovFa05XfThpGP2/L2Bvmg9XLtmsdzjCjVVXVrDt3AEE1kLB43cy7KYH9A7JLViO5LL/whH42aD0lQwGj7xJ75CEG/vitgvp8eshNp/jyw3//UPvcNpMS47fLjeKSjhH7LnDAEg8WIdlxUqsJxlSL8Tp/LLoXQJrodIfhlz9V73DcRvh0UnkmbTRVPszP9c5GuHuovYe1v5JklbUk5EEx0ucf829VPtAQB3k/fWv7LlkOCXz5+sdlnBDhb98C0BeogH/oBCdo3EvlhTtF6fPHhnpIs5c3ty5JNTXn+qx7KDsy09CEhwv4Vdhw7/uuAV2O/nTM6QlR7RYwN484FinWdF8gT37ARCXW6NzJMJdWc1mSp591lEmRVFV2ZefhCQ4XqJ2/wGUExfa7dQeyNYjHOGmbHV1JORp8ypF9r9A52jcz8Cx92BXIMYC23/7Ue9whBuq3X8A5cSes7Ivb5IkOF7CL60d6okZjsGAX7tUXeIR7mnd958RVgm1Rhgy7l69w3E7ie17kBer/b9l8ckLDgtxMn5p7RqVSZF9edMkwfESviYTEQ/e7/hiqIpC0L+myARtokUO/KCd688zKYRHJeocjXsqTg4GQN2xXedIhDvK862m7vgZBgwGEmbOkH15EyTB8SKJE/7G/vrvwEcXwdW2V1mwe4G+QQm34rNnHwCWlPDTrClOxtitGwAxuRU6RyLczYLdC7j/navwtUGFH2Q9fouUSTkFSXC8iLnCzO/ttfNUyUfArtqZsXoG5grpnCaa52jn2MBe/XWOxH31uOoOAOIPQ06WzEklmsdcYWbG6hl0Pqi1w+9MUfhX7RccCdU5MBcmCY4XyS7NZmeyluAc/ZLYVTs5ZV5SfFSclW1rvyfGAnZF6ywrzkyXvsMojNR2vusX/FvvcISbyC7Nxq7a6ZJbn+AkK7L/Pg1JcLxIalgqu5O0tzyxGMIqVAyKgZTQFJ0jE+5gx+I3AciLhcS07qdZW5zKoSStCnTdprVgkdpU4vRSw1IxqApd6n+c7khWZP99GpLgeBFTsIl/Dp9Bdox2vUsuZAzJwBQsndPEaWyYh9/2TQDUmOpgwzydA3JvvqnahH/huRUwq4e8nuK0TMEm7o4cR3QZ1BlgX6JB9t+nIQmOlxmbPpaSBD8AhmcHMzZ9rM4RCZdnyYXF9xNk1oZu+MTWwOLJ0vJwpiy59PbbAYCpQOFnHz/M30yR11OcVtSG3QDkxsHim76T/fdpSILjhZSO7QGIOVimcyTCLRRl8alfEPGHtf5bT3cPZUFwABRJuYEzUpRFqn8NxSHgY4fXbDGMTDaxYOt/9I5MuLodWmJcmhgsLTfNIAmOF0obdi0ACYUqlqJDOkcjXJ05MIxVh8IxAOYIKA4xMCMmCnOgDN84I1EdKfT1ZVuKljBetFklogxm7PlERjSKU4rOKwfA0KWzzpG4B0lwvFD/EX+iNAh8bfDrl2/oHY5wcflfLePub7SOjfElcPEmO3ZFIQervoG5q/Aksi+cjL1+ZvGLN6v8+982LtpYJyNixEmZD+7BVF9A/JxRt+objJuQBMcLGX18yU/U+lOUr1ki5/7FSVnNZgJe/uBYYT/grm/txJQpMnrjLCQnX8N5249NuG9Qtdc1qTJAx6iEK9vw+UsYVDgcDt0GXa53OG5BEhwvZUsMBCAo54iM4hAnVbv/ANjtDZYZVXgocbz0ATgL4YWVGE4oKGRUIfxQlT4BCde2YR6G9d8BUGKywe/SX6s5JMHxRpZc2odorTbRZgN2u11GxYgmaUVaT6jSajAwfKg0kZ8Nv7R2YDhh9ysFE0VT6kcxKoU+APjF1sr+upkkwfFGRVl0C6mk1gdCq+BgpR+oNhkVIxrxNZk42C3y2AIp7NcqfE0mEmbOOFb8FuR1FU0rysJmsxNn1g7XyZFVsr9uJklwvFFURwKNCuZ4bfe6ryQIFCNEddA5MOGKKq3ayI09vcKlsF8rihg3jr03nwtAURjyuoqmRXVkb0UgAVao9IP0wGrZXzeTJDjeKDwJRr9CTVwdABWH/WD0LG25ECeIy68FwHDhedLC0Mp63XA3ANGlsG/7Bp2jES4pPIntVVoyU5Bgx89olP11M0mC4636jcd2ziAAggt8oN94nQMSrmjLmu+JLAebAgPH/FXvcDxOardBmKO0/zcuelffYITLsuVWAFCeFAaTN8v+upkkwfFiPa75GwBxRZCza4vO0QhXtGPphwDkx0Jcskwu5gxHErTCmzXbNuobiHBZcXlaK6p/nyHSctMCkuB4sfSeFzp+Pf7+v7f0DUa4JPvO7QAU108rIFqfrYM2n1B4rkXnSIQr2rF+JVFlWivqgKulFbUlJMHxcocStcKb1Zvl/L9oLCK3vl5ZR+nQ6CxJ52mTtiUU2KmqkPpwoqFtX30AaK2oSWnn6BuMm5EEx8sd/fUYl1WM1Sx1cMQxlqJCEgq1kXYdLpaqxc4yaNRtVPiDvxV+/ep9vcMRLsbwx2YAymJlluuWkgTHy3XyawdA/BGVPZcMp2T+fJ0jEq7i14Vv4mMHSzD0HXaD3uF4LL+AIPJN2q64YPV3OkcjXEnJ/Pl03qpN09B1a7Xsn1tIEhwvZjWbCVmw/NgCu5386RnSkiMAKF6/EoACkxGjj4/O0Xi2iuQIAPz2H9Q3EOEyrGYz+dMzGtSBk/1zy0iC48WaqjOE3U7tgWx9AhIuJfBAAQCVqTE6R+L5gnr2ByC2fs4hIWT/fPYkwfFiUg9HnIzNZiM+X5sIMqLPUJ2j8Xz9x/wVOxBjgV2bVukdjnABfmntUE9cKPvnFpEEx4s56uHUt4GqQNC/pshstYLNq74mvALqDHDumLv1DsfjJaWdQ0F9Q9mWr+foG4xwCb4mE+bY4w7RUgeuxdokwZk9ezZpaWkEBAQwePBg1q5de9J133nnHS644AIiIyOJjIxkxIgRjda/7bbbUBSlwWXUqFHO3gyPFDFuHJue/zN2tHO844tnsWD3Ar3DEjrbk/kZAPmxCpHxKTpH4x2KErRRMtbtMummgPk7viCwQjtF9d6lBna/N1XqlbWQ0xOczz77jClTppCRkcGGDRvo3bs3I0eOpLCwsMn1ly9fzs0338yPP/7I6tWrSUlJ4bLLLiM3t2Fp+FGjRpGfn++4fPLJJ87eFI9krjDzbPFnZMdp1zvl2ZmxegbmCunI5s3sO3cCUJIYpHMk3sPWsT0A4XmlOkci9GauMPPG0plEVGqtqD/0UXhs9yzZL7eQ0xOcl19+mYkTJzJhwgS6d+/Om2++SVBQEO+/3/R8Dx999BH33HMPffr0oWvXrrz77rvY7XYyMzMbrOfv74/JZHJcIiMjnb0pHim7NBu7amd3knaeKj1Xxa7aySnL0TkyoafI/EoAlM5SnqGtpF50NQAJBSrlpSX6BiN0lV2aTXqu1nqzLx6sPorsl8+AUxOc2tpa1q9fz4gRI449ocHAiBEjWL16dbMeo7KyEqvVSlRUVIPly5cvJy4uji5dunD33Xdz5MiRVo3dW6SGpWJQDOxKrE9w8lQMioGUUDkt4a2Ksn7DdEjr3pg+Qua/aSsDL/0T5QHgVwcbPnwULLmnv5PwSKlhqaTnat/Boz8+Zb/cck5NcA4fPqyNxoiPb7A8Pj4eczPH8j/00EMkJiY2SJJGjRrFvHnzyMzM5LnnnmPFihVcfvnl2Gy2Jh+jpqaG0tLSBhehMQWbyBiSQVaS9lHomA/T+j6EKVg6snmlDfPY/+rV+NihJAR6BhTrHZHX8PHxo8CkHcyq130Ns3rAhnk6RyX0YAo20b0+v92dqGBQDGQMyZD9cgu59CiqZ599lk8//ZQvv/ySgIBj01TfdNNNXH311fTs2ZMxY8bw1VdfsW7dOpYvX97k4zzzzDOEh4c7LikpkgUfb2z6WN6ZsFibLr4O4rYd0jskoQdLLiy+n8Ji7btWFG/H+M0D0pLQViy5GGNrALAe9gXVDosny+vvhSxFh0iuL5My/PxbWXrdUsamS7mUlnJqghMTE4PRaKSgoKDB8oKCAkynGer24osv8uyzz/Ldd9/Rq1evU67boUMHYmJi2LNnT5O3T5s2DYvF4rjk5Mh5zBMlR6Zhrp8uvvDXZTpHI3RRlAWqnbrDvgDUxVlBtUHRXp0D8xJFWcRGVQEQXmDEbDTK6++lfl30Dj52KA2CsVdMlZabM+TUBMfPz4/+/fs36CB8tMPwkCFDTnq/559/nieeeIIlS5YwYMCA0z7PwYMHOXLkCAkJCU3e7u/vT1hYWIOLaKw8KRwAX5ku3jtFdWR+SAixedpuYWFCAAtCQyFKKom3iaiOZCUasCsQXQrTy00sUsLk9fdCRb8tB46WSfHVNxg35vRTVFOmTOGdd95h7ty5bN++nbvvvpuKigomTJgAwPjx45k2bZpj/eeee47HHnuM999/n7S0NMxmM2azmfJyreBYeXk5//znP/n111/Zv38/mZmZXHPNNXTq1ImRI0c6e3M8WuA5fQCIMdfoG4jQhdnHyKbd4YRVa9enfqmyMjcCs49R38C8hNnHyNOmKIpCtOv/+J9Kx09DOPDVEn0DE20uIFvro1qZHK1zJO7N6QnOjTfeyIsvvsj06dPp06cPGzduZMmSJY6Ox9nZ2eTn5zvWf+ONN6itrWXcuHEkJCQ4Li+++CIARqORP/74g6uvvprOnTtzxx130L9/f3766Sf8/f2dvTkerc+VWtIZVww5P74n5/69TE7WRm5acWxyeIMKd35r42DWJh2j8h7ZpdlElNqJLju2zKBCxVMvS4FFLxOXbwUgvHt3nSNxb21SInjSpElMmjSpydtO7Bi8f//+Uz5WYGAgS5cubaXIxPHadR3I8iiIL4K8/2aQsnIqjH4F+o3XOzTRBkxFKuUnLDOqEF/cqCKOcILUsFQSixVH9eijlPoCizJFv3fYN/9RosrArsDQI5/DhiGyDz5DLj2KSrQxSy5lcdpQ+6JifxnF4WVMXfs2Ku6nGhRMXfroEY7XMQWbuPnSKdhPzHCkwKL3sOSS98NcAMwxKuHGOtkHnwVJcMQxRVkERNcCoByqb9yTURxeo9JXaXhwNRhInDlTWg7a0NVDJhD48GRHoqkqihRY9CZFWViK/ACorP+xKfvgMycJjjgmqiOJkVoP01izAZsKKEYZxeElfl30DkYVSgMh+f336fRDphT300GHv/yV/fWz126/KFXeA28S1RGfQ9qoqaD6H5uyDz5zkuCIY8KT6HDdDGp8IagW9lUGwuhZEJ6kd2SiDRSv/wkAc4KR0KFDpNVAR6XtIrR/CqRzsTepNIYQV6Alt6kR1VpyI/vgMyYJjmggcMhfyYvXvmAb1f7Suc2LBGRroxkrk6NOs6ZwtoBu2uSmMmWDd1n71fv410GFP7S782OYvFn2wWdBEhzRSGliqPbP/vxTryg8SoxZG5oa2rO/zpGIXlf8BaifsiFri87RiLZSsEabFDffZMCv83BpuTlLkuCIRny7anMvRJmrdI5EtJVdf/xCdCnYgX6j79Q7HK/X4ZwhHIrQ/v990bu6xiLaztFZ5I/OKi/OjiQ4opHul/4JgPjDYM5pur6X8Cxbv9WGphZEQ2LaOTpHIwAOm7TOppVbNugciWgrR09JBp5z6vqLonkkwRGNdBt4KUfCtA/H+kXv6B2OaAM12zcDUGSS2cBdRW2q1sk7OLdI50hEWziw6w9ii7X/e19+m66xeApJcESTChO0eXDsK36SaeK9QFiuBQBb+xSdIxFHxQy4CACT2Yatrk7naISzbf3kdQAORUD77ufqG4yHkARHNCnYEAxApz+K2XPJcErmz9c5IuEstTXVmArsAMQPHqFzNOKowVffRa0RQqphw4/y/fNkJfPnk/aJNk1DTAmyv20lkuCIRqxmMyk7LMcW2O3kT8+QlhwPtXbphwTWQrUvnHvVHXqHI+qFRsRijtOmbNi/4kudoxHOYjWbyZ+e4ahBpoDsb1uJJDiikdr9B1BOLEpUX/BPeJ7cn78GID9eISAwROdoxPEsCUEAqHuydI5EOEvt/gNgtzdcKPvbViEJjmjEL60dGE74aEjBP49l3HcAOG7+I+EylPTOAETkV+ociXAWv7R2qMoJFVZlf9sqJMERjfiaTCTMnHGs4B8Q9K8pMnW/h4qsn+/It3M3nSMRJ+p40bUAJBxSsRwp0Dka4Qy+JhMHescdW2AwSIHVViIJjmhSxLhxrBilfcH2xcPVtldZsHuBzlGJ1nYodx+mw9r/3S77k77BiEZ6X3gtpUHgY4dfF72tdzjCCRbsXsBOpRCAX7rC7vemSoHVViIJjmiSucLMl+20I1/yYVDqbMxYPQNzhXR88yRr//c2BhWKQ6H7oMv0DkecwOjjQ0G8EYDiDT/pHI1obeYKMzNWzyA9X2sv/7Wrgcd2z5L9bCuRBEc0Kbs0m/xIlbIA8LNBWgHYVTs5ZTl6hyZaUekfawAoMPnoHIk4mYr64qf+2XLQ8zTZpdkYa22kag047E5UZD/biiTBEU1KDUvFYDCyJ1Hr/NYpT8WgGEgJlYngPEnQQW3PWpsUqXMk4mRCeg4AIDbfCpZcnaMRrSk1LJWOBdopyOJgtBnkZT/baiTBEU0yBZvIGJLBngTtenqeSsaQDEzB0vHNY2yYR5zZBkCnwCzYME/ngERTBnWOxw5El8Kh53vL++RBTMEmhuVphTX3JCoYDEbZz7YiSXDESY1NH0t6F23K8C55KmPTx+ockWg1llxyv5hKRDnYFOgSUgGLJ0sLgaux5BK/5lkORWl9NPaUBMj75GESDpYBYE0MZ+l1S2U/24okwRGndO5VfwMgvhiy92zWORrRaoqy2FwaAIA5ViXEqIJqg6K9OgcmGijKAtVOebzW0pZtCcRsQN4nDxJrtgIQf84QablpZZLgiFNq330QhyK0/39f/K6usYjWs6B0N5vKtFmLtyYZWBASDIoRojroHJloIKojKAYK4+tnpTrsy8iURBaU7tI3LtEqdv3xCzEWsAP9r75T73A8jiQ44rQOm/wAqNy6QedIRGswV5iZselVuuZoB828SJgRE4V51BMQnqRzdKKB8CTMo57ky/b+AHTOVYksVZmx6VUZSuwBtn47F4DCaEhI665zNJ5HEhxxWrWpWrNpSG6RnPv3ANml2Vy8wUp6vnZ9/I8qF/2hktNukL6BiSZlpw6kY76KCgRYYfYbdi7aWCdDiT1A7fZNABTV/4gUrUsSHHFayWnRAMSb7dj+r4eM4nBzyVWBTFyqOqoXG1S461s7SZUBusYlmibvl4faMI+wvGIAwiItsl91AklwxKlZchlQ8i1WI4RWwcEqHxnF4ebCCysxnFAt3qhC+KEqfQISpyTvlwey5FK36H7iCrRDcHJ4texXnUASHHFqRVkEGOwUxmp72P2WQBlt4+b80tqhnrhQqhe7LL+0dmA4YVct75d7K8pif6UvQTVQ4wOdgqtkv+oEkuCIU6sfxVETqw1TLSvyk9E2bs7XZKI0+LgFUr3YpfmaTCTMnIFq0E5SqUDY1MnyfrmzqI5klwQCUBin4mtA9qtOIAmOOLXwJBj9CsFRtQD4HfKB0bNktI0byz+wg9AK7X/lsX/Q6YdMqV7s4iLGjaPDd99RHgAKsNkmHYzdWngSJSVhAFhj67TkRvarrU4SHHF6/cYTcuVDAMQXKpR3vErngMTZWL/4PQxodW+63nKXtAS4iYDkZPKStMriJRt/0TkacbZCC+oAqOvUDSZvhn7jdY7I87RJgjN79mzS0tIICAhg8ODBrF279pTrf/HFF3Tt2pWAgAB69uzJN9980+B2VVWZPn06CQkJBAYGMmLECHbv3u3MTfB6fa+4i/L6yuJrvnpH73DEWSjbvA6AQyZfnSMRLVWVHAOAf3ahzpGIs1F8KBfTIe3/tFETpeXGSZye4Hz22WdMmTKFjIwMNmzYQO/evRk5ciSFhU1/QX/55Rduvvlm7rjjDn7//XfGjBnDmDFj2LJli2Od559/nldffZU333yTNWvWEBwczMiRI6murnb25ngto48PZpP2cTm0brm+wYizEnTwCADVKXE6RyJaKqRnfwDi6qf3F+5pzaK38bGDJQh6DLlC73A8ltMTnJdffpmJEycyYcIEunfvzptvvklQUBDvv/9+k+u/8sorjBo1in/+859069aNJ554gn79+vH6668DWuvNrFmzePTRR7nmmmvo1asX8+bNIy8vj4ULFzp7c7xaRVIkAL4H8nSORJwpm81GvFlrGo/se67O0YiW6n/VndiBqDLYufEnvcMRZ6j4d+0UY4HJiNHHR+doPJdTE5za2lrWr1/PiBEjjj2hwcCIESNYvXp1k/dZvXp1g/UBRo4c6Vh/3759mM3mBuuEh4czePDgkz6maB2B3XoDEF1Qq3Mk4kxtXbOE8Aqtgvig0X/VOxzRQglp3SjU5t1k25L/6BuMOGP+OQUAVCZH6xyJZ3NqgnP48GHtF2N8fIPl8fHxmM1N11Exm82nXP/o35Y8Zk1NDaWlpQ0uouV6XTkBgPgiyN69SedoxJnYnfk5AOZYiIpP0TkacSaOmLS6VDU7tpxmTeGqjlYQD+k5QOdIPJtXjKJ65plnCA8Pd1xSUmTHfibadxvgqCy+460XsJ4koRSuq27XDgCKEwJ1jkScKVtaMgCheRadIxFnYvePi49VEB89Ue9wPJpTE5yYmBiMRiMFBQUNlhcUFGA6ydBUk8l0yvWP/m3JY06bNg2LxeK45OTIHBJnyhqgDVNN+Wo9ey4ZTsn8+TpHJFoiLK8MAHv7djpHIs5U/KDhAJjMdqy1NTpHI1qiZP58rPc8CGjzGQX9Jq1wzuTUBMfPz4/+/fuTmZnpWGa328nMzGTIkCFN3mfIkCEN1gdYtmyZY/327dtjMpkarFNaWsqaNWtO+pj+/v6EhYU1uIiWs5rNJJhtxxbY7eRPz5CWHDdRVVFGQqFWpCF5yOU6RyPO1OArb6fGB4Jq4bdlH+kdjmgmq9lM/vQMlPo6KQrI/tPJnH6KasqUKbzzzjvMnTuX7du3c/fdd1NRUcGECVp/jvHjxzNt2jTH+vfffz9LlizhpZdeYseOHTz++OP89ttvTJo0CQBFUZg8eTJPPvkkixYtYvPmzYwfP57ExETGjBnj7M3xarX7DzgqGjvY7dQeyNYjHNFCa775AH8rVPrBwJF/1jsccYYCQ8Ixx2vfxJyfvtY5GtFctfsPgN3ecKHsP53K6ePTbrzxRg4dOsT06dMxm8306dOHJUuWODoJZ2dnYziukNzQoUP5+OOPefTRR3nkkUdIT09n4cKF9OjRw7HOgw8+SEVFBXfddRclJSWcf/75LFmyhICAAGdvjldzFP07/ksqRf/cRsGaZcQDZpOB/gHSB8edWRJCILcMZd8+vUMRzST7z7anqKraqLCwpystLSU8PByLxSKnq1qoZP588h59DAVQFQh+dCrtbrlD77BEM8wf15dztlSzaXAEN82VKRXc2fwZf+acT34jNw5GrNyudziimX5+5G6iFyzXrtQXuZU6cC3TkuO3V4yiEq0nYtw4fu/hB8APPeFq26ss2L1A56hEc0SZtZm+/bp21zkScbbSR2gHxfjD2rT/wvUt2L2AT2tWAnAgBna/N1WSGyeTBEe0iLnCzKr22ky4KYfBrtqZsXoG5grpKOfKzDl7iD+s/d/9slv0DUactR6Dr8QSBD52WLNIasO5OnOFmRmrZ9ApTzth8kcHhcd2z5L9ppNJgiNaJLs0m12JWgfHtAIw2lTsqp2cMhl678p+X/AKBqAoFLr2v0TvcMRZMvr4UGjSpmwo/20ZWKQVx5Vll2ZjV+2k52sJzu5ERfabbUASHNEiqWGpHIo0UBqoVRZPKwCDYiAlVCZPdFkb5qFs0EbblMTbYcM8nQMSrcGaoM1oHHjwEMzqIe+rC0sNS8XfqpBaX2N6d6Ii+802IAmOaBFTsImM8x5nT4LWipOep5IxJANTcNOTLAqdWXJh8f3YD/sCYIyphcWT5Re/u7Pkkhqsnd4ILzCCapf31YWZgk38ubIPPnYoDobicIPsN9uAJDiixcamj0VN0CqLDzpoZGz6WJ0jEidVlAWqnYgC7aseEGUF1QZFe3UOTJyVoiw6h1ZiB6JL4QeCMBuQ99WFxe3KAyDfZGDpuO9kv9kGJMERZySse18A4uqLxgkXFdWRD33CiSzXKog/2DWcBaGhENVB78jE2YjqSLgfFNQXo55bF8XIlEQWlO7SNy5xUgHZ2vkpa3KstNy0EUlwxBnpU19ZPK4YDuxcr3M04mTMPkZ+OxwCQF4UVPkbmBEThdnHqHNk4qyEJ2Ee9SQ76jv8D91uJ6IMZmx6VUbmuKijFcRDpYJ4m5EER5yR1K79HZXFf/9qjq6xiJPL/+Q/3LWkvv7UEbh4kx07qoze8ADZqQMx1k+Ke+FW+Pe/bVy0sU7eWxe0Y+MKoku1CuL9pIJ4m5EER5yxwyZtwj/rlrXSudEFWc1mAl7+wFE/TAHu+tZOTJkiozc8QHJVIOdvOzYRvUHV3t+kSilZ42p2fP0uAIXRkNCui87ReA9JcMQZMyQEARCSZ5Fhqi6oqeJ+RhUeShwvfQA8QHhhJYYTCu0YVQg/VKVPQKJpG+bhs1UrjVIZVyf7yTYkCY44M5Zc0gP3AxBdaMBul2GqrsYvrR2qckL9d4OB4UNv1Scg0aocxRuPJ8UbXUv9NA0+h7Q+bwFRVtlPtiFJcMSZKcoiPbgSqxFCq2B/tb8MP3YxviYTB3vGHltQX9zP1yStN57A12QiYeYMjjbiqCDvr6spyqLObie2fpqGlIgq2U+2IUlwxJmJ6oifj4HCWG33esASCIpRhh+7mFKbBYA93ULo9EOmFPfzMBHjxrHr2j4AmKOR99fVRHVkT2UgQbVQ4wsdgqtlP9mGJMERZyY8CUa/Qm2sDYDyI34wepa2XLiMaHMNAHXn9pdf9h6q05jbAIgrgiPm/brGIk4QnsQOazoAhXEqPkaj7CfbkCQ44sz1G091594A+B/ygX7jdQ5IHO/gvi3EHdH+73n5X/QNRjhNj8EjKQnROhiv/d/beocjTmDNKwegzBQMkzfLfrINSYIjzkra8D8BYDoEJUfydI5GHO/3Re9iAA6HQ6deQ/QORzhRgckHAMvGX3WORJwoMr8aAKVrb2m5aWOS4Iiz0vvCqykLBF8brFn8jt7hiOOUb9kAwGGTr86RCGerStE6kwfkHNI5EnG8Q3lZmA5r/3e97BZ9g/FCkuCIs2L08aHApA2BLNrwk87RiOMFHywCoCY1QedIhLOF99Za6OLMdaCqp1lbtJV1i97GqIIlGLoOvFjvcLyOJDjirFUkaRX//OuLyQn92erqMJm1DuBRAy7SORrhbIPGTMSmQGQ5bFnzrd7hiHqWP9YCUGjywXDinEXC6eQVF2ctqOdAABJyrFjNUujPFWxc8V9Cq8BqhHOvkdo3ni7GlIY5Rvt/57JP9Q1GOITsra8gHhujcyTeSRIccdZ6+qUBEFEBey6+hJL58/UNSJC1fAEA+bEKYRGxp1lbeILixEAA6nbu1DkSAVD8xRd03K+VSum2xiz7RR1IgiPOitVspvq1N44tUFXyp2dIS47e9mQBYEkM1jkQ0VbUDu0BCMsv0zkSYTWbyZ+ecazQrYrsF3UgCY44K00VdMRup/ZAtj4BCQAi8isBUDql6xyJaCvJ518FQEKBSkWZRedovFvt/gMoJ3b2lv1im5MER5wVKfjnekoO55FQqO1cOw67TudoRFsZeOmfqPQH/zpY89W7eofj1fzS2tFoLJvsF9ucJDjirDgK/tVXrVYB/wcnSVkAHa1d/C4+digNgt4XXqN3OKKN+Pr5k2/SdumF637QORrv5msycTjiuAVS6FYXkuCIsxYxbhw73vw7tUZQgEmH/82C3Qv0DstrHZ2PqMBkxOjjo3M0oi2VJ0UC4Ls/V+dIvNunm+YRplVoYPaVBna/N1UKoepAEhxx1swVZmYceIPd9bOQd8qzM2P1DMwV0qFOD/7ZBQBUJkfrHIloawHdtdpwMfk1OkfivcwVZj5Z8gL+dVAeACt7Kjy2e5bsD3UgCY44a9ml2dhVO7uStNNUnXNV7KqdnLIcnSPzTrH5VgDCup2jcySirfW5cgIAccVwcMUcsEhLTlvLLs0mPVcbeLEnQUFVFNkf6kQSHHHWUsNSMSgGR4KTnqtiUAykhKboHJn32b9gOtGlYAfOK/oMNszTOyTRhtK6DeBQhPZ/7vzHYFYP+Qy0sdSwVNJztS7GR/eJsj/UhyQ44qyZgk1kDMkgK1GrSZV8GKa0vx1TsHSoa1OWXHJ/mAPAoWiVcGMdLJ4sv+K9iSWX0nitRMeRYj9Q7fIZaGOmYBNd6xOc3UlacpMxJEP2hzpwaoJTVFTELbfcQlhYGBEREdxxxx2Ul5efcv377ruPLl26EBgYSGpqKn//+9+xWBrO6aAoSqPLp5/K9OR6Gps+li/+8h2HwrUPVeRve/QOyfsUZVFyxA+A8vqDHKoNivbqGJRoU0VZ+EXXAqAcqq8iL5+BNrV700riSrT//zx6BkuvW8rY9LG6xuStnDrE4pZbbiE/P59ly5ZhtVqZMGECd911Fx9//HGT6+fl5ZGXl8eLL75I9+7dOXDgAH/729/Iy8tj/gnTXM+ZM4dRo0Y5rkdERDhzU0QzmIJN/JLgR6ylloqtv+sdjveJ6ojhUP1XOrpO+6sYIaqDfjGJthXVkcSIGiCQmAIDeQYjiSryGWhDm7+dRzegIApGDpCRU3pyWoKzfft2lixZwrp16xgwYAAAr732GldccQUvvvgiiYmJje7To0cP/vvf/zqud+zYkaeeeopbb72Vuro6fI4b8hoREYFJ5hRwObVpSbBjHyEHi/UOxet8nr2CToVao+wb6UHUGq2MvfhpCE/SOTLRZsKT2Dr8erp+t4yQapgQksBfe13OWPkMtJma7VsAOJIQoHMkwmmnqFavXk1ERIQjuQEYMWIEBoOBNWvWNPtxLBYLYWFhDZIbgHvvvZeYmBgGDRrE+++/j3ritNhCF3GDhgNgMtuxHpZm8bZirjCz8L9PE1gLVb6QE6swIzYac5fL9A5NtCFzhZmnj6xgb7x2/aI/VF7b8Z0MUW5DYXmlAKjtG/+IF23LaQmO2WwmLi6uwTIfHx+ioqIwN7Pg2OHDh3niiSe46667GiyfOXMmn3/+OcuWLeO6667jnnvu4bXXXjvp49TU1FBaWtrgIpxjSFoINT4QUg17nx8qIzjaSP4n/+Ffn2r9bgKsMGyzDNX3RkenbKjWumJx7a8qr8+2kv/ph/oG5iWqVr9Foln7sd2H9bL/01mLE5yHH364yU6+x1927Nhx1oGVlpZy5ZVX0r17dx5//PEGtz322GOcd9559O3bl4ceeogHH3yQF1544aSP9cwzzxAeHu64pKTIcD2nsOQSuOxhCuO1L3hOib+M4GgDVrOZgJc/cHyZFeCub+3ElCkyNNXLpIalElOm0GvfsWUGFQJemiOVrJ3NkkvWfzMIsEKlH7QPrpL9n85anOA88MADbN++/ZSXDh06YDKZKCwsbHDfuro6ioqKTtt3pqysjFGjRhEaGsqXX36Jr6/vKdcfPHgwBw8epKam6dk7p02bhsVicVxycuRXrVMUZYFqxxarTTRXecRPRnC0gaYquhtVeChxvAxN9TKmYBMPJYxvvGOXStbOV5RFbonW7+ZwvB2jguz/dNbiTsaxsbHExsaedr0hQ4ZQUlLC+vXr6d+/PwA//PADdrudwYMHn/R+paWljBw5En9/fxYtWkRAwOk7am3cuJHIyEj8/f2bvN3f3/+kt4lWFNURFAMRUTWAHyEFRuglo3iczS+tHSgKHN8PzWBg+NBb9QtK6Gb4ebeyxzCnYdIrlaydL6ojtYe1c4NqnIxidAVO64PTrVs3Ro0axcSJE1m7di2rVq1i0qRJ3HTTTY4RVLm5uXTt2pW1a9cCWnJz2WWXUVFRwXvvvUdpaSlmsxmz2YzNpvUvWLx4Me+++y5btmxhz549vPHGGzz99NPcd999ztoU0VzhSTD6FTpFaC1p8YcVzEMelFE8TuZrMpF/XsdjC6RysVfzNZlImDmDo+muCvJ5aAvhSYQWaJOdxkRWa8nN6Fmy/9ORU+fB+eijj5g0aRLDhw/HYDBw3XXX8eqrrzput1qt7Ny5k8rKSgA2bNjgGGHVqVOnBo+1b98+0tLS8PX1Zfbs2fzjH/9AVVU6derEyy+/zMSJE525KaK5+o0ntuNwdn0/gqhSWLMjj2tkII/TFdYdIgHYn+bLiA++k4OZl4sYN47MZW/TfUUO+1MUuksla6fbvfln4utnx0i66TnoebEkNzpzaoITFRV10kn9ANLS0hoM7x42bNhph3uPGjWqwQR/wgWFJ1GY4EdUaS0VmzfoHY1XCMvVRgaW9uwkyY0AIGLYFbDiLWIPqVhrqvD1D9Q7JI/2xzdz6A4URkK38+X0sCuQWlTCKWrbab9cgmXCP6erLCt2DE1NuehqnaMRrmLI1Xc4pmxYu+QDvcPxeLU7tgIywZ8rkQRHOEXsudp5qQSzHWttlc7ReLZfF72JvxUq/WHQZbfoHY5wEUHBoeSbtF38wZ+/0Tkazxda34pa1yFN30CEgyQ4winOvfpOao0QWgVrl8lkV85UuOZHAPITjPj4nXpKBeFdSpMjADDulSHizlRVfqwVNekCaUV1FZLgCKcICgnBHKd9vHJ++krnaDyb34F8AMpTonWORLga/3P6ABCTX6tvIB7u16/fJrAWqn1h0ChpRXUVkuAIp7EkhwMQsvmAzKLqLKpKXL4250Zo73N1Dka4mj6j7wQgvgj2bl2tczSe68jy7wAojDHg6++nczTiKElwhNPEGLUJITtmWdlzyXBK5s/XOSLPs2XNt0SXgl2BAdf+Te9whItJ69qXgkjt/z++nqNvMB6qZP58uv+YB0BKvl32cy5EEhzhFFazmYQ1u48tsNvJn54hLTmtbMdSbRoGcwzEJ7XXORrhig4naqN6qrf9oXMknsdqNpM/PQOl/roCsp9zIZLgCKeo3X+gYekAkHo4TmDbtROAosRgnSMRrsrWMQ2AsIOl+gbigZqqAyf7OdchCY5wCr+0dmA44eMl9XBaXURuhfZPerq+gQiXlXLBVQAkFqhUlJXoG4yH8UtrR6OpaWU/5zIkwRFO0VQ9nLdGKSwu+0XPsDxKceFBEgu1Vzj90ht0jka4qoEj/0yFP/hb4df/vaV3OB5lcdkvbDyulqZqUKTulwuRBEc4TfXl5/P0jVrxuWpf+LEnzFg9A3OFnJ9uDasXvoGPHSzB0PO80XqHI1yUr58f+Qna97Bw3Q86R+M5zBVmZqyeQWD9CPwvz1W49x4fqi8/X9/AhIMkOMJpskuz+SNNm2E30AqphWBX7eSU5egdmkco27ASgIIEI0Yfp5aVE26uIiUKgMB9uWDJ1Tkaz5Bdmo3RaqOjNg0VP/Q2cDhUlf2bC5EERzhNalgqitHIziRtjEHXgyoGxUBKaIrOkXmADfMIyS4EICCmAjbIbNHi5OLSYgCINdtgVg/5vLSC1LBUOuaDrw1KgqEgEtm/uRhJcITTmIJNZAzJYGdyfYKTo5IxJANTsJyfPiuWXGyL7ifGrH19EyKrYfFk+WUummbJZWD1CuwKRJVCXrVRPi+twBRs4pKcIAB2JCsYDEbZv7kYSXCEU41NH0uPPlcA0O2gyjXtpU7LWSvKIrvKl7BKsBqhS0glqDYo2qt3ZMIVFWURaqzDHKt1SN9jCZLPSytJytZGMdalxrH0uqWMTR+rc0TieJLgCKcbccMD1Bkgshw2rvxC73DcX1RHtlq0X475cSr+RkAxQlSHU99PeKeojqAYqIq3AWAu8sfs4yufl7NUW11JQr42B07HoddIy40LkgRHOF1kjIm8eO001Z5Mmcb8bC0oXMPeEi3B2ZhiYEFoKIyeBeFJ+gYmXFN4Eox+hUKTdjAOKPBhZEoiCwrX6ByYe1vz7fuEVGsjRIdePVHvcEQTJMERbcKSFAqAcdduOfd/Fo4OTe2WrZ1uyI2CGbHRmLtcpnNkwpWZu1zGR520pLiDGWKLbDJlw1nKXfk/APJNBgKCQ3SORjRFEhzRJsLTtGGq0Xm1MorjLGSXZnPpOitJRdr1vy5VuWhjnQxNFaeUXZrNOfttqIBRhVfessvn5mxsmEfw3gMAGGKrZX/moiTBEc5nyWWguhYA0xGFQqsiozjOUHJVIBOWqY7ifgYV7vrWTlJlgK5xCdeWXBXIX5cc97lBPjdnzJKLuvh+Isza5IlxMTKK0VVJgiOcryiLKN86DkVqp1V2lgTLKI4zFF5Y2ehLa1Qh/FCVLvEI9xBeWInhhKJJ8rk5Q0VZZNf4EGMBuwJdw2QUo6uSBEc4X/0ojnKTNoqj+Ii/jPo5Q1LcT5wJKX7biqI6sqe+k39BrEqQj132Zy5KEhzhfPWjOEJitKItfoU+MurnDFlspdiU4xYYDFLcT5zW0eK3xyc5JaP6y+fmTIQnUVQUBkBNfJ2W3Mj+zCVJgiPaRr/xhF2bAUCiWeFw4oU6B+Sefv1yNj4qlAZCygdz6PRDJhHjxukdlnADEePG0emHTHJN2m5/f410MD5TEXl1ANi69ITJm6HfeJ0jEk2RBEe0mV6jbqM0SKvd8uvC1/UOxy2VbdQ6a+el+hFy7rnyC1y0iK/JxOFuiQAEHijUORr3dGDXGhIPaf93GfeQtNy4MElwRJsxGAwUJPoBYPn9V52jcU9h2RYAajql6RuIcFvR540EIDHXTm1Vhc7RuJ/1i97BoMKRcEjvc67e4YhTkARHtKmq9lql3ZCcYp0jcT+lRfkk5WldjFMvkdNS4swMHfNXanwhtArWfPOO3uG4neqtfwBwKDFQ50jE6UiCI9qU6Xyt2GZinp3q8iKdo3Evq798Hf86KA+EQZfepHc4wk0Fh4Q6+uHk/vytztG4n7CD5QDUpXfSORJxOpLgiDZ17ug/U+MLIdXwy1dv6B2OWyla9zMAeUm++Pj56hyNcGdl7WIB8Nubp3Mk7qW4cC/J+VoravtL/6RzNOJ0JMERbco/KJA8kzYDaPk332I1Sy2c5go+cBiAqg7SqVGcnbAB2ijGhIN12OqsOkfjPtZ++BL+dVDhD30vHq13OOI0JMERbc7HXytMl772CHsuGU7JfKkwfjrVlaUk5WrVoE3nXaFzNMLdnXf9JKxGiKiA9d9/pHc4bqFk/nxS3v4BgKAaKFv4pc4RidNxaoJTVFTELbfcQlhYGBEREdxxxx2Ul5ef8j7Dhg1DUZQGl7/97W8N1snOzubKK68kKCiIuLg4/vnPf1JXV+fMTRGtxGo2k5xlObbAbid/eoa05JzGqoVvEFQLlX4wdMxEvcMRbi48Oo48kzZj5L4fFugcjeuzms3kT89w1PJSQPZbbsCpCc4tt9zC1q1bWbZsGV999RUrV67krrvuOu39Jk6cSH5+vuPy/PPPO26z2WxceeWV1NbW8ssvvzB37lw++OADpk+f7sxNEa2kdv8BlBNrDdjt1B7I1iUed1H4yzIA8pKM+PlLgURx9iwpkQD47DmgcySur3b/AbDbGy6U/ZbLc1qCs337dpYsWcK7777L4MGDOf/883nttdf49NNPycs7dce2oKAgTCaT4xIWFua47bvvvmPbtm18+OGH9OnTh8svv5wnnniC2bNnU1tb66zNEa2kqZo4NgUy7Vt1isg9BO7XfilWtIvTORLhKQL7DAIgLrcW1EYVzsRxMtVt2JUTFkotL5fntARn9erVREREMGDAAMeyESNGYDAYWLNmzSnv+9FHHxETE0OPHj2YNm0alZWVDR63Z8+exMfHO5aNHDmS0tJStm6Vg6Sr8zWZCPrXFI7+FlKBty838NjuWZgrpLm3KXVF+0jM1QqVRg8ernM0wlMMHncfNgViLLDtf8+DJVfvkFySucLMY7tnsbrrsQzHpkDQv6bITOIuzmkJjtlsJi6u4a9NHx8foqKiMJ/ivOWf/vQnPvzwQ3788UemTZvGf/7zH2699dYGj3t8cgM4rp/scWtqaigtLW1wEfopuKQnr1yj7SxKguHHXgp21U5OmdTGaWTDPPY8M4TQKqjxhfM6R+sdkfAQ8ckdyK/fRRcsmQ2zesCGefoG5YKyS7Oxq3YC6gebfddX4d57jBQO76VvYOK0WpzgPPzww406AZ942bFjxxkHdNdddzFy5Eh69uzJLbfcwrx58/jyyy/Jyso648d85plnCA8Pd1xSUlLO+LHE2UsNS2VDug9WI0RWgKkYDIqBlFB5Xxqw5MLi+8kp0vrcFJjsBH3/iPzSFq3DkkutSTtqVxzyB9UOiyfL5+sEqWGp+NgVuuVop/EyexsoCTfK/soNtDjBeeCBB9i+ffspLx06dMBkMlFY2LCYW11dHUVFRZha0Kw3ePBgAPbs2QOAyWSioKCgwTpHr5/scadNm4bFYnFccnKkpUBPpmATj1z0OLu1mn/0OKCSMSQDU7A09zZQlAWqndpCrX6XPd4Kqg2K9uocmPAIRVlExVQDEJqnzU0ln6/GTMEmJlT1IagGygMg22SQ/ZWb8GnpHWJjY4mNjT3tekOGDKGkpIT169fTv39/AH744QfsdrsjaWmOjRs3ApCQkOB43KeeeorCwkLHKbBly5YRFhZG9+7dm3wMf39//P39m/2cwvnGpo/lP+3+D3IOc94+hbHpY/UOyfVEdcSGgah87eATGFsLihGiOugcmPAIUR3pGllFHqHEFStkEsQ5PlZM8vlqJHbTfgCyk4wsuf47SW7chNP64HTr1o1Ro0YxceJE1q5dy6pVq5g0aRI33XQTiYnaT/fc3Fy6du3K2rVrAcjKyuKJJ55g/fr17N+/n0WLFjF+/HguvPBCevXSzndedtlldO/enT//+c9s2rSJpUuX8uijj3LvvfdKEuNmYuo7zCYftFFnrdE5GhcUnsSchGFElIPVCFO7h7PgvNshXGYyFq0gPInIsf9Hfv3v1U9qohiZksiCwlMPAvFGIfuPAGDtmCLJjRtpcQtOS3z00UdMmjSJ4cOHYzAYuO6663j11Vcdt1utVnbu3OkYJeXn58f333/PrFmzqKioICUlheuuu45HH33UcR+j0chXX33F3XffzZAhQwgODuYvf/kLM2fObPX4bTYbVqtMY+4sg669m5zPVxJaB+vmP0vfEbdBaPxp7+ctDlUeonB/KfaEBA7GQlSID28d3szAohxig07fiuoJ/Pz8MBhkwnVnMXe5jD9SniXpkMr5W+3sTlSYsXoGQxOHyoG8nqW4gOQ8bdxn6nkjdI5GtISiqt43AUJpaSnh4eFYLJYGc+wcpaoqZrOZkpKStg/Oy1QV5OFjgzp/lUCjHYIiwS9E77BcQm2ZBaWswnG9LACq/SA6MBp/o3e0VhoMBtq3b4+fn5/eoXiktflrWf2P27hso3YYsCvw1uUG/vzgBww0DdQ5OteQ+cL1JL63hfJA6HeNGePVr0C/8XqH5bVOd/w+nlNbcNzV0eQmLi6OoKAgFOXEGZ5Eq6irpczHim8V1PpBWFB9uY2oJPDx7gOa3Wqldp8VAoIaLM+PVkiOSMPX6PnVxO12O3l5eeTn55OamirfQydIrgpkxKZjv3ENKtz1rZ2oSTJbNgCWXCo2bwD8OJxkw0j9SLOOw+VUsRuQBOcENpvNkdxER8ucI05VY0UNUKHGiK8N/IwKBgXwVcDLyxHY6upQmjg1kxgUQ2hwqA4R6SM2Npa8vDzq6urw9fX8pK6thRdWYjmhDd+oQvihKpC+xlCUhU++9rkLjKufKf/oSDNJcFyenNw+wdE+N0FBQadZU5w1oz8BBjuqov1yrLYbHMu9nXKSDvOhId6VdB89NWWz2XSOxDM1VTpFShAcc0j1IylfaznsFFV/ulhGMroNSXBOQprD24CPH0pECtb6H+a1NgOEp3j96SkAg68v1hPaV30TEzF4WSuGfA+dy9dkImHmDNT611kFTBnTpQRBvVVff4RfHZQGqyQF10/TMHqWtN64CTlFJfQVHIPN/wjUWlGtCgTH6B2RS7DbrBjrGy3qoiMIjon3uuRGtI2IceOo6pzOkRtuwgjsCbMg3Ys1FRu0KUzMyf4ot32ltdxIcuM2pAXHy6mqyl133UVUVBSKojgmVmxLvqFRAPjVgq1OhuUDlBUXYFC1US3B8d7XciPaVkKv3uQmaoeDrO/m6xyN64jI1uoWWrt2hfYXSHLjZiTB8XJLlizhgw8+4KuvviI/P58ePXq0eQzBEdHY6/vhlBcXnP4OXqCuvAwAq58i88CINlHcQZuDyn+P1KICOJi1jtR87f/Oo+/UNxhxRmTP6cFqa2tPu05WVhYJCQkMHToUk8mEj0/Lz1qqqkpdXd2ZhAhoc51Y/bQ+AHWVZWf8OJ7EWKOdn7IHSIdr0TaiLxwNQHKOnaryYp2j0d/aBa/hY4fiUOgxdLje4YgzIAmOBxk2bBiTJk1i8uTJxMTEMHLkSLZs2cLll19OSEgI8fHx/PnPf+bw4cMA3Hbbbdx3331kZ2ejKAppaWmANv/IM888Q/v27QkMDKR3797Mn3+s2Xr58uUoisK3335L//798ff35+eff272/TIzMxkwYABBQUEMHTqUnTt3Yq8fNWSssbF48WIGDhxIQEAAMTExXHvttY7HqKmpYerUqSQlJREcHMzgwYNZvny581/cNmStqcKv/kydf4T0SRJt48Lr/0alH4RUw89fvKx3OLqr3rwFgIKUYGlFdVPyrjWDqqpU1ta1+eVMJpmeO3cufn5+rFq1imeffZZLLrmEvn378ttvv7FkyRIKCgq44YYbAHjllVeYOXMmycnJ5Ofns27dOgCeeeYZ5s2bx5tvvsnWrVv5xz/+wa233sqKFSsaPNfDDz/Ms88+y/bt2+nVq1ez7/evf/2Ll156id9++w0fHx9uv/12/MK14c8/fL+Sa6+9lstHjuT3338nMzOTQYMGOe47adIkVq9ezaeffsoff/zB9ddfz6hRo9i9e3eLXytXVV5cgALYjBAUEq53OMJL+AcGkpui9fU6vPpHnaPRmd1OzP4qAJT2XXUORpwpGUXVDFVWG92nL23z5902cyRBfi17i9LT03n++ecBePLJJ+nbty9PP/204/b333+flJQUdu3aRefOnQkNDcVoNGKqHxZaU1PD008/zffff8+QIUMA6NChAz///DNvvfUWF110keOxZs6cyaWXXtri+z311FOO6w8//DBXXnklRr8AVAWef/ttrh81imk33YRvfDw+UVH07t0bgOzsbObMmUN2drajYOvUqVNZsmQJc+bMabCd7kytr81W62cgRIZJizZU1aU9ZO0ifG+R3qHoatesx0ku1P7v8s0GSobMJ2LcOH2DEi0mCY6H6d+/v+P/TZs28eOPPxIS0ri2U1ZWFp07d260fM+ePVRWVjoSl6Nqa2vp27dvg2UDBgw4o/sdrQwPkJCQAEBBXh7xKvyxcycTrrsOAGteHobQUMcIos2bN2Oz2RrFXVNT41GzTvvUaoX9lECZbFK0rU5X3QbfPEJKnkrBwV3EJzfeR3g6q9lM3dtf4PhpoarkT88g+PzzZX4gNyMJTjME+hrZNnOkLs/bUsHBwY7/y8vLGT16NM8991yj9Y4mFicqLy8H4OuvvyYpqeGQSP8TZtc98bmae7/jp9w/OpGbrboagMAT1lVraqF+/fLycoxGI+vXr8dobPjaNJXEuaOq8hJ86/trB0XF6RuM8Dp9h13D6rBHiCqFXz55iWv/+ZbeIbW52v0HaNRuardTeyBbEhw3IwlOMyiK0uJTRa6gX79+/Pe//yUtLa3Zo6O6d++Ov78/2dnZDU4rOet+Ryl+flBTQ4/OnVm+Zg3j6zsWK/7HZjXu27cvNpuNwsJCLrjgghY/hzuoKjlMIGD1gbAAacERbctgMJCfGkjUlipqN67XOxxdfG/dRDo0THKkfIVbkk7GHuzee++lqKiIm2++mXXr1pGVlcXSpUuZMGHCSWv7hIaGMnXqVP7xj38wd+5csrKy2LBhA6+99hpz58496XOd6f2OshngULjCI3ffzefffssTs2fzS+FeNm7d7GiB6ty5M7fccgvjx49nwYIF7Nu3j7Vr1/LMM8/w9ddfn9mL5GKU6hoA6vxb3nonRGtQevYEIPZABVi8a04cc4WZ2b+9hoJWtgLApkDQv6ZI640bcr9mCdFsiYmJrFq1ioceeojLLruMmpoa2rVrx6hRo0457PGJJ54gNjaWZ555hr179xIREUG/fv145JFHTvl8Z3o/AKvNSm0g9LlwIB++9BJPv/0WL77/HmFhYVx04bEWoTlz5vDkk0/ywAMPkJubS0xMDOeeey5XXXVV818YF6VWHMa3Vtut+htroeKwlK4QbW5Ivy4Uf7KWhMOQ91wfEse9BP3G6x1Wm8guzaZPltYHbkcSfHaRAXOkwovDe9FO59hEyynqmYxFdnOlpaWEh4djsVgICwtrcFt1dTX79u2jffv2BAQE6BSh97HarOwq3kVArUpikdaicyBOoXNkZ3yNXlCmoK6WqvztYDGiKhAQYcWgAHHneHXxUfk+tjFLLszqQWZmPImFCvkXVXJJYhlM3uwVZQrMFWZ+HHcJffapzLvEwFeDDRgUA0uvW4opWFpwXMGpjt8nklNUwiX4Gn1JDEmkxk/BroDRDjH2IO9IbgBsNdTUaV9Hqy9aclO/XIg2U5QFqp2aJG2myeLCAMwGoGivvnG1EcORI3TP1n7z/95RwaAYyBiSIcmNm5IER7iMyIBI0iM7U1tftsG3sgrqTl9uwhMU26qx1WnbXeYPxUdPIRqlVINoQ1EdQTFQmKz10TPlGBiZnMCC0l06B9Y2Vs97Ej8bHAmDmTe/x9LrljI2fazeYYkzJAmOcCm+Rl+U+g62xho7FG7V+qJ4MKvNyqGyQgLrG2uq/BXyfHywhiV59ekpoYPwJMyjnuS1LsHU+EBUOVy4GV776RXMFWa9o3OuDfNg028AlKZYGWTeKS03bk4SHOFa6moJNmhz4vhZoVZVwJLj0S051qIjpBxSHcNS/a1aE3mtf/DJ7ySEk2SnDqTW10BBhHb9nm/svD7bSv6nH+oal1NZcqlbdD9R2dq4mzhTFSye7HWjyDyNJDjCtdhq8DWo1NWP76uq75fiqX1R7FYrSkHDFqpYC/jYwc8grTei7aWGpRJTppB83MfSoELAS3Owmj20Facoix2V/sRYwGqEnpEVoNq8pu+Rp5IER7iW+j4ndl+tFcNuVRos9zRqTdOJm8k32ns6WAuXYgo28VDC+MYHh/rZfD1SVEf2HtIm1ixIsuPvo4JihKgOOgcmzoYkOMK1+PhBeAp+vtpcFL61CjYP7oui+DeduIWGeE5tLeF+hp93K5w4V5Ynz+YbnoThoPZd9E2s0ZKb0bO8Ymi8J5MER7ie4Bj8E7o4houXVXnm6SkAg68vtQENv4a+iYmOAqNC6MHXZCJh5gzHbL4qkDBzhsfO5rt/12ra1Xe3iR99nzbvj5dMbujJJMERLsngG4C1fri4rbxM52icSFVR7VprVU2QH/5duuATFaVzUEJAxLhx5N5zCwAVAWAcNkjniJzn109ewscOhyOg23UPSMuNh5AEx4MMGzaMyZMn6x3GaS1fvhxFUSgpKTnlemqQdk7cp9aOp064XV1pwb9+gJh/fILTWm4URWHhwoXNXr+575HwbBfd9U/KAyGkGn788Em9w3GeLTsBKOggPy48iSQ4wmUFRWvN4X5WqCw7onM0zlFZXAho1cMDg0Od9jz5+flcfvnlrfqYjz/+OH369GnVxxSuxS/An+wO2nQFlWvX6hyNc1SXFZCyrw6AoPNb9zsi9CUJjnA5NpsNu92Of0Ag1vrh4tUWz0xwlCqt+aYuwLl9bkwmE/4n6dAsxKkYzr0AgKSsGupqq3SOpvUt/+JZosqh1gcuunWy3uGIViQJjjNZcmHfSl0mi6qpqWHq1KkkJSURHBzM4MGDWb58eYN13nnnHVJSUggKCuLaa6/l5ZdfJiIiosE6//vf/+jXrx8BAQF06NCBGTNmUFdX57hdURTeffddrr32WoKCgkhPT2fRokUNHuObb76hc+fOBAYGcvHFF7N///4Gt3/wwQdERESwaNEiunfvjr+/P9nZ2dTU1PDIS/9Hx+HDSe3Sl8GDBjXahlM53fZlZWVxzTXXEB8fT0hICAMHDuT7779v8BhNndqJiIjggw8+AKC2tpZJkyaRkJBAQEAA7dq145lnngFAVVUef/xxUlNT8ff3JzExkb///e+Ox7HWVjlOT/mGHxs19frrr9OjRw/H9YULF6IoCm+++aZj2YgRI3j00Ucd15vzPh2/Hb/88gt9+vQhICCAAQMGOJ5j48aNDbZ1/fr1DBgwgKCgIIYOHcrOnVpT/gcffMCMGTPYtGkTiqKgKAoffPDBabdZuJ9Lbn+UGh+IscCKL17UO5xWZ1m+AoC8BD+Cw0J0jka0KtULWSwWFVAtFkuj26qqqtRt27apVVVVxxba7apaU96yy5q3VfXxCFXNCNP+rnm75Y9ht7douy666CL1/vvvV1VVVe+880516NCh6sqVK9U9e/aoL7zwgurv76/u2rVLVVVV/fnnn1WDwaC+8MIL6s6dO9XZs2erUVFRanh4uOPxVq5cqYaFhakffPCBmpWVpX733XdqWlqa+vjjjzvWAdTk5GT1448/Vnfv3q3+/e9/V0NCQtQjR46oqqqq2dnZqr+/vzplyhR1x44d6ocffqjGx8ergFpcXKyqqqrOmTNH9fX1VYcOHaquWrVK3bFjh1pRUaHeeeed6uABA9RlH3ygbvnmG/XpBx5osA2n0pzt27hxo/rmm2+qmzdvVnft2qU++uijakBAgHrgwIEG2/fll182eOzw8HB1zpw5qqqq6gsvvKCmpKSoK1euVPfv36/+9NNP6scff6yqqqp+8cUXalhYmPrNN9+oBw4cUNesWaO+/fbbjscpystSKzdvVsu2blbtx73Xf/zxh6ooilpYWKiqqqpOnjxZjYmJUW+88UZVVVW1trZWDQoKUpctW9ai9+nodlgsFjUqKkq99dZb1a1bt6rffPON2rlzZxVQf//9d1VVVfXHH39UAXXw4MHq8uXL1a1bt6oXXHCBOnToUFVVVbWyslJ94IEH1HPOOUfNz89X8/Pz1crKytNuc0s1+X0Ube5/V/RUt3Xpqn50+7l6h9Kqij79WN3apau6rUtXdWuXrmrxF1/oHZI4jVMdv0/k1ATnyJEj6p/+9Cc1NDRUDQ8PV2+//Xa1rKzspOvv27dPRRuR2Ojy+eefHwu6ids/+eSTZsfV4gSnplxLVNr6UlPe7G1S1WMJzoEDB1Sj0ajm5uY2uH348OHqtGnTVFVV1RtvvFG98sorG9x+yy23NEgAhg8frj799NMN1vnPf/6jJiQkOK4D6qOPPuq4Xl5ergLqt99+q6qqqk6bNk3t3r17g8d46KGHGiU4gLpx40bHOke3YU9mplq5ebPjcvHgwerDDz542teiOdvXlHPOOUd97bXXGmzfqRKc++67T73kkksaJChHvfTSS2rnzp3V2traJp/ryO4tauXmzeqRrG0NltvtdjU6Olr9on5n26dPH/WZZ55RTSaTqqpa8ubr66tWVFSoqtr89+nodrzxxhtqdHR0g8/4O++802SC8/333zvW+frrr1XAcb+MjAy1d+/eLdrmlpIExzV8Pu0mdVuXrup3F3TVO5RWU5ufr27t2k3dVp/gbOvSVd3Wrbtam5+vd2jiFFqS4Dj1FNUtt9zC1q1bWbZsGV999RUrV67krrvuOun6KSkp5OfnN7jMmDGDkJCQRh0k58yZ02C9MWPGOHNT3MrmzZux2Wx07tyZkJAQx2XFihVkZWUBsHPnTgYNajjs88TrmzZtYubMmQ0eY+LEieTn51NZWelYr1evXo7/g4ODCQsLo7BQ6zy7fft2Bg8e3OBxhwwZ0ihmPz+/Bo9zdBt6X3UVsYMGOS4/rV/Pzl07TvsaNGf7ysvLmTp1Kt26dSMiIoKQkBC2b99OdnbzZ2u97bbb2LhxI126dOHvf/873333neO266+/nqqqKjp06MDEiRP58ssvHaeN7NZq/Gu1kWHGkLAGj6koChdeeCHLly+npKSEbdu2cc8991BTU8OOHTtYsWIFAwcOJKh+lFlz36fjX5tevXoREBBw0tfmqOPfk4SEBADHe9uUU22zcF+D/jINuwLJhfDHf5/wiBpNmas+RDlxdKYnz9bshXyc9cDbt29nyZIlrFu3jgEDBgDw2muvccUVV/Diiy+SmJjY6D5GoxHTCRNJffnll9xwww2EhDQ8NxoREdFoXafxDYJH8pq/fmkezB4Eqv3YMsUI966BsMbbfcrnPQPl5eUYjUbWr1+P0WhscNuJr+PpHmfGjBmMHTu20W3HHxx9TxjarCgKdrv9xLucUmBgIIqiOK4f3YZVn33WaBtKUoOx2qxnXcpg6tSpLFu2jBdffJFOnToRGBjIuHHjqK09VthTUZRGQ9StVqvj/379+rFv3z6+/fZbvv/+e2644QZGjBjB/PnzSUlJYefOnXz//fcsW7aMe+65hxdeeIEV3/yX2rJCDHYjdgVCgxrP0jxs2DDefvttfvrpJ/r27UtYWJgj6VmxYgUXXXRRg9eqOe/TmTj+vT36/pzqvT3pNq9Y0ehzItxHuy69WJoIqbmQ+/X79NryMox+xW0nwzNXmHkubx6zAeX4Gzx5tmYv5LQEZ/Xq1URERDiSG9A6RhoMBtasWcO111572sdYv349GzduZPbs2Y1uu/fee7nzzjvp0KEDf/vb35gwYUKDA2SrUhTwa0Fl55h07cu/eLJWsO3otN8x6c6J7wR9+/bFZrNRWFjIBRdc0OQ6Xbp0Yd26dQ2WnXi9X79+7Ny5k06dOp1xLN26dWvU6fjXX3897f0c24CN81PbO5aXBIMSqlBrrz1lgtOc7Vu1ahW33Xab47NYXl7eqAN0bGws+fn5juu7d+9u1CoSFhbGjTfeyI033si4ceMYNWoURUVFREVFERgYyOjRoxk9ejT33nsvXbt2ZfOaH+nQqSf+QJ2/iqH0IASENyhHcdFFFzF58mS++OILhg0bBmhJz/fff8+qVat44IEHHOu29H3q0qULH374ITU1NY6RVSe+Ns3h5+eHzWZrtLzJbd68mX79+rX4OYSLsORiSKmG3ADI8YNUu7Z/6zjcLSfFyy7NpsbHjsqxBMemgPWBCR47W7M3clqCYzabiYuLa/hkPj5ERUVhbmZF2vfee49u3boxdOjQBstnzpzJJZdcQlBQEN999x333HMP5eXlJx2tUVNTQ81xRQ1LS0tbuDVnoN947ctftFcr2NaGO4HOnTtzyy23MH78eF566SX69u3LoUOHyMzMpFevXlx55ZXcd999XHjhhbz88suMHj2aH374gW+//bZBkjh9+nSuuuoqUlNTGTduHAaDgU2bNrFlyxaefLJ5k3797W9/46WXXuKf//wnd955J+vXr3eMQGrONtz1938wZfr9nNeuK+UFxSxdv4akfp3pfGPnU96/OduXnp7OggULGD16NIqi8NhjjzVqnbjkkkt4/fXXGTJkCDabjYceeqhBS8TLL79MQkICffv2xWAw8MUXX2AymRwjrWw2G4MHDyYoKIgPP/yQwMBAUpMSMNZqcRjri4piq2mQ4PTq1YvIyEg+/vhjvvrqK0BLcKZOnYqiKJx33nmOdVv6Pv3pT3/iX//6F3fddRcPP/ww2dnZvPiiNjqmJT8S0tLS2LdvHxs3biQ5OZnQ0FA++eSTJre5Xbt2zX5c4YKKsugWV04ZAaQcNHDYaiTGt77athsmOKlhqZy7Q8UA7I+FDy41UBhl5JObbtU7NNGaWtrB52gH0VNdtm/frj711FNq586dG90/NjZW/fe//33a56msrFTDw8PVF1988bTrPvbYY2pycvJJb8/IyGgyzmZ3MnYTx4+iqq2tVadPn66mpaWpvr6+akJCgnrttdeqf/zxh2P9t99+W01KSlIDAwPVMWPGqE8++aSjI+tRS5YsUYcOHaoGBgaqYWFh6qBBgxqMiuE0nXBVVVUXL16sdurUSfX391cvuOAC9f3332/Uybipzr9HtyG1Xarq6+ujmmJj1dEjhqsr1yxv1utxuu3bt2+fevHFF6uBgYFqSkqK+vrrrzd4DVVVVXNzc9XLLrtMDQ4OVtPT09Vvvvmmwfa9/fbbap8+fdTg4GA1LCxMHT58uLphwwZVVVX1yy+/VAcPHqyGhYWpwcHB6rnnnqt+v/RbtSxno1q5ebNasWWzWndwg6rmblBVa02j+K+55hrVx8fH0THfZrOpkZGR6rnnNh7J0tL3adWqVWqvXr1UPz8/tX///urHH3+sAuqOHTtUVT3Wyfjoe6Sqqvr777+rgLpv3z5VVVW1urpave6669SIiAgVUOfMmdP0Nh/XUbml3Pn76FFKDqrq4xHqD+d1Ubd16ap+cnd7Nf+JaG25m/rfCK2D8bS/dVd7ze2l/nfXf/UOSTRDSzoZK6rasjnwDx06xJEjp550rUOHDnz44Yc88MADFBcXO5bX1dUREBDAF198cdpTVP/5z3+44447yM3NJTY29pTrfv3111x11VVUV1c3OZlZUy04KSkpWCwWwsIadvCsrq5m3759tG/f/qz7L7ibiRMnsmPHDn766Se9Q2mkpq4G667dGO1QExVARFxqiyuMu8L2FVcXU2nOJaocKv3BEGojMjQJgmN0iwngo48+YsKECVgsFgIDA3WN5Xje/H10ORvmMW/Wkwxca2RNF4X/G+tDxtDHGZveuO+Xq9uS+T7KvS9gALa9Npnzhl6DKVhOTbmD0tJSwsPDmzx+n6jFp6hiY2NPm3CANlKmpKSE9evX079/fwB++OEH7HZ7o1E1TXnvvfe4+uqrm/VcGzduJDIy8qQztfr7+8ssrk148cUXufTSSwkODubbb79l7ty5/Pvf/9Y7rCb5+/hT5a9grFJRK6ugcCuEp5wyMXC17bParOSV55FcrV2v8gOLjw8hAeG0dffbefPm0aFDB5KSkti0aRMPPfQQN9xwg0slN8K1mLtcxn/PeYGBa+vonaXSM8vGa2WPMzRxqHslBxvmsf+jJ+mIP3kJdq6LDgR3il80m9P64HTr1o1Ro0YxceJE3nzzTaxWK5MmTeKmm25yjKDKzc1l+PDhzJs3r8Ew1T179rBy5Uq++eabRo+7ePFiCgoKOPfccwkICGDZsmU8/fTTTJ061Vmb4rHWrl3L888/T1lZGR06dODVV1/lzjvv1DusptXV4u9bB1VG/GoURk2cxM9rfwel8UwHjzzyCI888ojLbV+trZbwCpV1a9Yz5u67AVAVUE7YhvLycqfHYjabmT59OmazmYSEBK6//nqeeuoppz+vcF/ZpdnsjVcpC4DQavjX53bsip38wA8x3eEm+19LLuri+/HZFw+AsV2NW3eWFqfmtAQHtGbvSZMmMXz4cAwGA9dddx2vvvqq43ar1crOnTsbjUp5//33SU5O5rLLLmv0mL6+vsyePZt//OMfqKpKp06dePnll5k4caIzN8Ujff7553qH0Hy2GgKMdioMRox2mPXc4/hYKyGyHfg1HPoeFaVVBHa17fNVFaLLoN855/Dr/PmO5Ya0FPz82rbl5MEHH+TBBx9s0+cU7i01LJWYcgMh1cdGzhlUCHhpDtYrb3WP0UdFWeys8aVdvoId6BNfqo10ddPO0uLUnJrgREVF8fHHH5/09rS0tEZzjAA8/fTTPP30003eZ9SoUYwaNarVYhRuwuiPooDdX8VYpRAflUBkkBXiure4L45eDLVWbEBgQAAdU4/NteGX2h5jSAumIRBCB6ZgEw8ljEfhvYY31E+O5xYJTlRHtueH0hUwJ9k5J7B+Go+oDnpHJpxAim0K9+DjB+Ep+Ptqw7j9a6A2ON5tkhuAioriJpcr/u6zDcK7DT/vVjCccNhwo8nx7MGxBO3Vvm+B7aqOzVEmrTceSRIc4T6CY/BL7IbNCIoKZeUVekfUInUVjeP1TUzEIDP8CjfhazKRMHMGR9vdVcCU8Zh7tN4AK758ltQCbVK/Drc/D5M3u+1szOL0JMERbkXx8aM2QEsIlMoaaNksB7qx1lQSUK3FWhsTiV9ae/y7dMGnvr+QEO4iYtw4At55GxvaLMCb2KV3SM12cOlCALJT/DCdf5O03Hg4SXCE2/GL0kZABNRCVWWRztE0T9nhXAwq2AwQGpeAMSRYWm6E2+pwwQXsb6+d6sn7eqG+wTSTtbwA084qACqHnq9zNKItSIIj3E5wWDh19aepqgsLsR9X/NJVGSq0iSZrg3wxnNiHQQg3ZB12CQBp26ooK25BMWKd/PjOgyQfgjoFhv01Q+9wRBuQPa0HGTZsGJMnT27Wuh988AERERFOjcdZFEXB7qO1fgRU2KjZuZO6opa15Dz++OP06dOnRfdpyet7vIqyI/jXFygPiHaPvgpCnM6oSU9RFgiR5fDdmw/rHc4plcyfT/JbawEwquCzaqXOEYm2IAmOOCtpaWnMmjWrwTJnJ092qxW/moatNta8vBa15EydOpXMzMzWDg1FUVi4cGGDZdVHCgGo9YWg0PBWf04h9BAYHMSB7hEAKL+sh30rwZKrb1BNsJrN5D823VE1XAHyp2dgbWbRZ+G+JMERbkc9rq7Y8crKT10j7XghISFER0e3VkgnZa84hF+VNjGawd8OFYed/pxCtJXEcdrM4OlZdszvXguzesCGeTpH1VDmqg8bD0aon7tHeDZJcJzIXGFmbf5azBVt/0uhuLiY8ePHExkZSVBQEJdffjm7d+9utN7ChQtJT08nICCAkSNHkpOT47gtKyuLa665hvj4eEJCQhg4cCDff/+94/Zhw4Zx4MAB/vGPf6AoCoqisHz5ckfRxqPLHn/88RbFdCJVVYmNjWV+/ey/ir8/g8eNo/3FFzvW+WXDBmJNqVjKLACUlJRw5513EhsbS1hYGJdccgmbNm1yrH/iKaq6ujr+/ve/ExERQXR0NA899BB/+ctfGDNmTINY7HY7Dz74IFFRUZhMJse2gdaaBXDttdeiKAppaWlUFeWxbdtORt1+O4k9hhBmSqN/v3789ttvp91uIVzdeZeMIj9OxccOv+eHgWrXSh+4SEuOucLMc3nzaDTW0o3m7hFnThKcZlBVlUprZYsun+74lJHzR3LHd3cwcv5IPt3xaYsfo4WF3hu47bbb+O2331i0aBGrV69GVVWuuOIKrMedxqmsrOSpp55i3rx5rFq1ipKSEm666SbH7eXl5VxxxRVkZmby+++/M2rUKEaPHk12tvbLZ8GCBSQnJzNz5kzy8/PJz89n6NChzJo1i7CwMMeyo3XCmhNTUxRF4cILL2T58uUAWMrL2blvH9U1NezcuxeA7zf9Ro8+PfAJ0Cbnvv766yksLOTbb79l/fr19OvXj+HDh1N0kr46zz33HB999BFz5sxh1apVlJaWNjrVBDB37lyCg4NZs2YNzz//PDNnzmTZsmUArFu3DoA5c+aQn5/Pup9/pLbGwO0PP4wpMZ513/yH9d9+xMNTJ+MrI6iEJyjKQu2kVY/12+3PmgB/zAa00gcuILs0m8AaOwo4khybAtUPTHCbuXvEmXNqqQZPUVVXxeCPT18B/WTs2HlqzVM8taZlxQzX/GkNQb5BLX6+3bt3s2jRIlatWsXQoUMBrS5YSkoKCxcu5Prrrwe0WmCvv/66o7r73Llz6datG2vXrmXQoEH07t2b3r17Ox73iSee4Msvv2TRokVMmjSJqKgojEYjoaGhmI7bWYSHh6MoSoNlzY3pZIYNG8Zbb70FwMqVK+nTpw+hUSEs2/QbXTp04Ndf1zFg6AD8air4ec3vrF27lsLCQkcV+RdffJGFCxcyf/587rrrrkaP/9prrzFt2jSuvfZaAF5//fUmi7326tWLjAxtBEZ6ejqvv/46mZmZXHrppcTGxgIQERGByWTisCUXf4tCTn4+t917G/GdOxJpt5N+7jluNQOzECcV1ZF+iWXkGANJPKTwoBJHdgpklO5iLBfoHR2p2eu4fJ02+/mGjrB4sIHCKCOf3HSrzpGJtiAtOB5o+/bt+Pj4OBIXgOjoaLp06cL27dsdy3x8fBg4cKDjeteuXYmIiHCsU15eztSpU+nWrRsRERGEhISwfft2RwuOM2I6mYsuuoht27Zx6NAhVqxYwcUXX8wlF1/Mj+vXUWu1svb3TVw6sD++pbls2rCe8vJyoqOjCQkJcVz27dtHVlZWo8e2WCwUFBQ0qGhvNBrp379/o3V79erV4HpCQgKFhYWN1rParFSXFKOocO9fxvPIPx/nihv/xlPv/JesAzmN1hfCLYUnUTN6JuvStS68162yEVEGMza9qsup+QYsudR99TgXbtXabv43xMiOVIX7LrgfU7C03ngDacFphkCfQNb8aU2z1y+oLGDMwjHYsTuWGRQDC69ZSHxQfIueV09Tp05l2bJlvPjii3Tq1InAwEDGjRtHbW1tm8fSs2dPoqKiWLFiBStWrOCpp57CFBXKay+9wurdW7BarQw5py8A5WUWEhISHKe0jne2o7tOPLWkKAp2u73RerVHCoku0/6ffvc9jLzhCr796Sd+WLGamU+/wKeffupoLRLCnWWnDqQoVPt/8C4YuNvGW5er5FyWo28iUZTF2pwwutWBOVblQWMhKTl1mC7qrF9Mok1JC04zKIpCkG9Qsy/tw9uTMTQDg6K9vAbFQMaQDNqHt2/R4yiKcprImtat2/+3d+dxUZX7A8c/MzAzbAKCyICCqCyiobiHmJBLpGXaZi43lzKXXKLN5aapdc3laqbpLbOEulladl1yRxT8iWsIhkuUilgqKMoOssyc3x/o6LDJmMMy87xfr3n58pznnPOcx+OZ7zyrP6WlpRw9ejcou3HjBsnJybRt21a3rbS0VK+za3JyMllZWfj7+wMQFxfH6NGjefbZZwkICECtVnPx4kW9aymVSjQazX231TRPVZHJZDz22GNs2bKF06dP07NnT9oHdqaouJh1P/xAp3btcLawoVCS06lzF9LS0rC0tMTb21vv06RJkwrndnBwwNXVVdeHBkCj0XDixIn75qs8hUJBSVER8mv6C2t2d/bilXEj2bVrF8899xwREREGn1sQ6qPmhdYM+OVuf0G5BON2amlWYFWHuYKbMhVNT5c1Bdv45dO1qAi1FrFyuBkRAY6RPOfzHLuf383asLXsfn43z/k8V2vX9vHxYdCgQbz22mscPHiQkydP8o9//INmzZoxaNAgXTqFQsGUKVM4evQo8fHxjB49mkcffVTXVOPj48P//vc/EhMTOXnyJMOHD69QW+Hl5cWBAwe4fPkyGRkZum15eXlER0eTkZFBQUFBjfNUndDQUL7//nsCAwOxs7NDrrSiV89gvt+8kx7dugBQUGRJ37D+BAUFMXjwYPbs2cPFixc5dOgQ7733XpWjl6ZMmcKCBQvYsmULycnJvPHGG2RmZhocZHp5ebEvKoq0jAwys7MpvHWLN+fP58Dx4xSnFXDsyDGOHz+uCyIFoaFzuFaAvNx4CAsJHK4X1k2GbtuxZg7OuZBnLdHZLUesHG6GRIBjRGpbNV3VXeukmjYiIoLOnTvz9NNPExQUhCRJ7NixQ6+JxcbGhunTpzN8+HCCg4Oxs7Njw4YNuv0ff/wxjRs3pkePHgwcOJCwsDA6deqkd50PPviAixcv0rp1a10n2x49ejBhwgReeuklXFxcWLx4cY3zVJ2QkBA0Gg2hoaG6baF9nkCj0dAztKxDo9UtieJbOezYsYNevXoxZswYfH19GTp0KKmpqbi6Vt5EOH36dIYNG8bIkSMJCgrCzs6OsLAwrKwM+xW6dOlS9uzbi2+/fgQNGYKFhQU3s7MZ+89/0qVrT4YMGUL//v2ZN2+eQecVhPpK6dUCyi0/IkGdDsMuKbiJ45FUAP7s1BzLV7aJlcPNkEz6O2ORG6icnBwcHBzIzs7G3t5eb9+tW7dISUmhZcuWBn+5CXVH0krkJ5/GQgP59nKaeN6/2as6Wq0Wf39/hgwZwocffljzfEhass6dwarcXIQKd3excvgDEP8fG4asjRu5+v4cuF3Dm2sNrbdvxNm9XZ3kZ9OKYbT5TyIaOdhv2oKnn+h3Yyqq+/4uT9TgCCZBJpdRbGcLgDJfS0lWhkFLN6SmprJmzRp+//13kpKSmDhxIikpKQwfPtygfGRn/KULbqTmzVB6tUTl5yeCG8GkOb7wAt77ommyahV5VtCoEHYumVQneZFu5VAalQhASitHEdyYMRHgCPVC//799YZ03/v56KOPanQOe9fmSIBCA6V/pRm0CKdcLicyMpKuXbsSHBxMUlISe/fuNaivjFRajJSVA8AtKzk2jo2xsLNFLib1E8yAQq3GpU9vLvYqqz1tEZdOVsKPtT6rceysEbS7PUF66/PZZN2eAV0wP6KJSjRR1QuXL1+msLDyTolOTk441aAGRFtSQlFycoXtKj8/4wcZ+Rnk37yMPNsCAJmbI1bOzY17TTMg/j82PDk3Mznbtwf2BXCh1y2eapYFA5fXSv+XrQc+x3vccvSGBsjleO+LFjMXmwhDmqjEPDhCvdCs2d8f2VB6q6DK7UqFEVfxLi2G7D8pKVSgAoqtJByKrkNpUzFjsWB27C0KKAy4hf1RKxwSrShQS9j8HA6t+xh1BFNafhpRWz7Fp/yO2wtrigDH/IgmKsFklFhUsV1WatwLa4rI1chR3Z7/0NpKo9suCGbn5nmCPG6SYwvOObA53blW1qdKufR/9E6oOOmmJBbWNFsiwBFMhlJlw3UH/XlrCpSgzPkT8jOMdt2sW3loCsqiq1xryLe8nQcLldGuKQj1llNrVAo5v3Uq6+TfIl7JOyVqtqbEG++aJ77hyqfTaHMFSuRlC2pC2Z+2770lam/MlAhwBJOhsFDQyMWdS01luqnjbYqhSCuD7D/LmpIesqIb11H9eQPV7QFbJZZwxdKSEvtmonlKME8OzUh78l982l1Fngqc8uC9HyRaT1pN6rqvHv71si9zacvbNDtS1kdr42MyJr1uwQcjLLmwdhotRrz68K8pNAiiD45gUhpbNcZOklGsuUixygJlkYzSfAs0jbRYaIoeatChLSlBezVdb5tTLuRaQbHKFjF2SjBXlzy7YntMhs09rbRyCfLnf0xJn6ceao2KdD2ZuN8aE1gANxpLTHBLZ2C+JR4vfom6zTMP7TpCwyNqcASTo1DYYCtJ2FmXIslAVQJZJZYPvclIqqJTs1IDSrmovRHMl6e9J+6ZsgpfMLLbHX4fpp+2LKP9ybImYvfOWbijoWtRKWq3zg/1OkLDIwIcM3Dx4kVkMhmJiYm1dk0vLy8++eSTWrueHkslOHhgIQfJuqzToVWejPyMywZN/nc/WZlXKt3+xcqv6dq560O7Tm2YO3cugYGBBh0TGhpKeHi4UfIjNGxqWzXD+r2FttxSbhKgaOb20K5zOTaSxhvPIQeue5fQqkmhWHNK0BEBjmCabJtA03ZYu3uhkZdVj8sz8ilKTqboxvW/d+7SYnIzUrHK1WATEMDW6GjdLrmbK7P++T7R92xrCN555x2j5Fkmk7F58+aHfl6h/nsmaAx2s95BumedKgn46atxkHLgb08AmLp2BdnjF+GeWXZez77jYZRYc0q4SwQ4gumyVIKFNRblRo5qr6aTlXX5gTodl+RdI+f6WYqu3NStoKxwd9ctyaBydsHOzg5nZ+eHcAO1pyHmWaj/Wox4FZ990Xh+/TV/tG2CHPDedJHDXw7h2OedSTu66oHOu3XfMvL+/ZluQj8ZUPhFJCXWPqLmRtARAY4RlaSlkX/kKCVpabVyPa1Wy+LFi/H29kalUuHp6cn8+fMrTXvq1Cnd8giurq68/PLLZGTcHUodGhrK1KlTmTZtGk5OTqjVaubOnavbL0kSc+fOxdPTE5VKhbu7O1OnTtW7RkFBAa+88gqNGjXC09OTL774Qm//9OnT8fX1xcbGhlatWjF79mxKbjchZWdnY2FhwS+//KK7NycnJx599FHd8d9++y0eHh7VlolUVNbL8a+0NEZNm0az4GCadOvGYyFPELdrA+RnMHr0aAYPHqx3XHh4uP6q5aGhvDbhVca+9TYt24by/NjxtAkLA+D5IUOwbGRHK5+yKcbKN/fExMTQrVs3bG1tcXR0JDg4mNTUspWOT548yeOPP06jRo2wt7enc+fOunuu8p4kCRcXFzbeMwV9YGAgbm53q/4PHjyISqWioKCsn1BWVhZjx47FxcUFe3t7evfuzcmTJ3Xpy+e5tLSUqVOn4ujoiLOzM9OnT2fUqFEVykmr1Vb5jHh5eQHw7LPPIpPJdH9/kHsWGi6FWo1t9270W/kV6a5a7G7BzYON+afKmTd3/Yet+z4x6HxpR1exf8sa3Q8MHSP07xEaNhHg1IAkSWgLCgz63PzuO8717sOl0aM517sPN7/7zuBzGLqKxsyZM1m4cCGzZ8/mzJkzfPfdd7i6ulZIl5WVRe/evenYsSO//PILu3btIj09nSFDhuil+/rrr7G1teXo0aMsXryYDz74gKioKAB++uknli1bxurVq/njjz/YvHkzAQEBescvXbqULl26kJCQwOuvv87EiRNJvmcphUaNGhEZGcmZM2dYvnw5a9asYdmyZQA4ODgQGBhITEwMAElJSchkMhISEsjLywMgNjaWkJCQastEplKRV1BA2JgxXElP58dPP+Xoxo1MGjeGW5K2bPi4tuLkYOVJksT3367HuVTBvm++YcXs2Wzf8j0AEV98xtWrVzl+/HiF40pLSxk8eDAhISH8+uuvHD58mHHjxiGTlf32HDFiBM2bN+f48ePEx8czY8YMFPdZVkImk9GrVy9d2WRmZnL27FkKCwv57bffdGXTtWtXbGxsAHjxxRe5du0aO3fuJD4+nk6dOtGnTx9uVrFW16JFi1i3bh0RERHExcWRk5NTaVNTdc/InfKIiIjQK58HuWeh4bMuSsMtOJMca2iVDis+1/L+91rDho9n/8X2/y3h5X0V341iQj+hPKMNE58/fz7bt28nMTERpVJJVlbWfY+RJIk5c+awZs0asrKyCA4O5rPPPsPH5+7k2zdv3mTKlCn8/PPPyOVynn/+eZYvX46dnZ2xbgWpsJDkTn+jR75WS/oHH5L+wYcGHeZ3Ih7Z7S+o+8nNzWX58uWsXLmSUaNGAdC6dWt69uzJxYsX9dKuXLmSjh076i1iuXbtWjw8PPj999/x9S1bfbd9+/bMmTMHAB8fH1auXEl0dDT9+vXj0qVLqNVq+vbti0KhwNPTk27duuldZ8CAAbz++utAWW3NsmXL2L9/P35+fgDMmjVLl9bLy4t33nmH9evXM23aNKCs1iQmJoZ33nmHmJgY+vXrx2+//cbBgwd58skniYmJ0aWtilyh4IeD/0dGZib/t349Tg5lSza09vQk106iVFtatkhmVUFOaTFoitBoivD2bMH8t96qkMTRyRl1FcNec3JyyM7O5umnn6Z169YAegt4Xrp0iXfffZc2bdroyrkmQkNDWb16NQAHDhygY8eOqNVqYmJiaNOmDTExMbrg7+DBgxw7doxr166hUpWNJFuyZAmbN29m48aNjBs3rsL5P/30U2bOnMmzzz4LlD0zO3bsqJCuumfExcWlrHwcHfXK50HvWWjgnFqT7SBnbT8Zb2yVdM1LZcPHl1Li0wSFX5dKm5hK0tIoPHWMTVtm02WfFUoNXHYCdSZYSGUT+jUSE/oJ5RitBqe4uJgXX3yRiRMn1viYxYsXs2LFCj7//HOOHj2Kra0tYWFh3Lp1S5dmxIgRnD59mqioKLZt28aBAwcqfUGbm7Nnz1JUVESfPn3um/bkyZPs379fb8XuO18258+f16Vr37693nFubm5cu3YNKKsRKCwspFWrVrz22mts2rSJ0lL9JRHuPV4mk6FWq3XHA2zYsIHg4GDUajV2dnbMmjWLS5fuVjGHhIRw8OBBNBoNsbGxhIaG6oKeK1eucO7cOb1mpKqcPneegMD2FLV0JNUFsm7Hwo3yZJRkKdDmF6LNy6Mo/W6/HI2mBE1JEcVpZ8i8noKsWEPHtm0rv4BF1bUPTk5OjB49mrCwMAYOHMjy5cu5evWqbv9bb73F2LFj6du3LwsXLtQr/+qEhIRw5swZrl+/XqFsSkpKOHTokK5sTp48SV5eHs7Oznr/5ikpKZVeLzs7m/T0dL2A1cLCgs6dKwb51T0jVXnQexYaOIdmeIbOJsdWRrnBVci0EjkRr3FlYUfiv5jMlQtJZTuyL5O64j3+ePxxLk+eTteoYpQaSGmlZcYr8rIJ/YbJubBqvJjQT6jAaDU48+bNAyAyMrJG6SVJ4pNPPmHWrFkMGjQIgG+++QZXV1c2b97M0KFDOXv2LLt27eL48eN06dIFKPulOWDAAJYsWYK7u7tR7kVmbY3fiZpPM16Sns6Fp57Wb/qQy2m1fRuKSpqMqrtuTVkbkDYvL4+BAweyaNGiCvvu7cdRvtlAJpOhvX1PHh4eJCcns3fvXqKionj99df597//TWxsrO646o4/fPgwI0aMYN68eYSFheHg4MD69etZunSpLn2vXr3Izc3lxIkTHDhwgI8++gi1Ws3ChQvp0KED7u7uNfr1b21tjaWFAg9XX4oLrqPUXKPUWg6FZfG9TC4va4a8nsk1zQ2UGiXF128gKy5Fk2WJFSCTwNaAMr5XREQEU6dOZdeuXWzYsIFZs2YRFRXFo48+yty5cxk+fDjbt29n586dzJkzh/Xr1+tqTqoSEBCAk5MTsbGxxMbGMn/+fNRqNYsWLeL48eOUlJTQo0cPoOzf283NTdekdS9HR8cHuqc7qvs3rsqD3rPQ8Km7T2JYfgna9asr9KE5He+Mcw7YEE3msmjinnImQ36ZXlutdL/EZZSNmOrT7gadrmr5U6nE48nZqLtPquU7ERqCetMHJyUlhbS0NPr27avb5uDgQPfu3Tl8+DBQ9qXo6OioC24A+vbti1wu5+jRo0bLm0wmQ25jU+OPqmVL3D6YB3eGR8rluH0wD1XLlgad504/jZrw8fHB2tq6RkN9O3XqxOnTp/Hy8sLb21vvY2trW+NrWltbM3DgQFasWEFMTAyHDx8mKSmpRsceOnSIFi1a8N5779GlSxd8fHx0HW/vcHR0pH379qxcuRKFQkGbNm3o1asXCQkJbNu27b79b+5o3749iYmJ5GbnYtvIHUXTtiid7gZyLo0bk3a7g3Wjm3JU2aX8ek9fIQBJDnJL/S9uhbs7CoUCjUZz3zx07NiRmTNncujQIR555BG+++473T5fX1/efPNN9uzZw3PPPUdERMR9zyeTyXjsscfYsmULp0+fpmfPnrRv356ioiJWr15Nly5ddP+WnTp1Ii0tDUtLywr/3k2aNKlwbgcHB1xdXfX6FGk0Gk6cOHHffJVXVfk8yD0LpuGZ3uF6w8clJEpk4JJz9wtJLkG7bTcIvSe4uUMGlPb/GvU/ttB1QrwIboQq1ZsAJ+32SKPynWJdXV11+9LS0mjatKnefktLS5ycnHRpKlNUVEROTo7ex9gcX3gB79vDI733ReP4wgtGvZ6VlRXTp09n2rRpfPPNN5w/f54jR47w1VcVO+9NmjSJmzdvMmzYMI4fP8758+fZvXs3Y8aMqdGXNZTVzH311VecOnWKCxcu8O2332JtbU2LFi1qdLyPjw+XLl1i/fr1nD9/nhUrVrBp06YK6UJDQ1m3bp0umHFycsLf358NGzbUOMAZNmwYarWawYMHExcXx4VLf/G/Pfs4enviw5Du3Tlx+jTrtm7lXGoqH65axZlz5/RPIpeQW0iovFvphoRbOjnh5eVFdHQ0aWlpZGZmVrh2SkoKM2fO5PDhw6SmprJnzx7++OMP/P39KSwsZPLkycTExJCamkpcXBzHjx/X66NTndDQUL7//nsCAwOxs7NDLpfTq1cvvfKCsh8BQUFBDB48mD179nDx4kUOHTrEe++9V+XopSlTprBgwQK2bNlCcnIyb7zxBpmZmQYF3UCF8vm79yyYBt3w8f8swWfQdQpCciukkQHF8rIam3tJcjnKtp2h5WNiSLhQLYMCnBkzZiCTyar93BnFUZ8sWLAABwcH3ed+Q4sfljvDI2ur49vs2bN5++23ef/99/H39+ell16qtD+Eu7s7cXFxaDQannjiCQICAggPD8fR0RG5vGaPhKOjI2vWrCE4OJj27duzd+9efv755xrPpfLMM8/w5ptvMnnyZAIDAzl06BCzZ8+ukC4kJASNRlNhyHb5bdVRKpXs2bOHpk2bMmDAAAICAli8ZAmWrmWdYPsFBzNj/Hj++cnHBA8fRl5+PsMHDtQ7hxxA1Qi5lQ0WdrbIbzfNLF26lKioKDw8POjYsWOFa9vY2PDbb7/x/PPP4+vry7hx45g0aRLjx4/HwsKCGzduMHLkSHx9fRkyZAj9+/fXNe/eT03LRiaTsWPHDnr16sWYMWPw9fVl6NChpKamVjrKDso6hQ8bNoyRI0cSFBSEnZ0dYWFhWFlZ1Shvd5Qvn797z4LpUKjV2PZ+CsVLy/BsXFxh1mOtDN4cL+PzAXKxOrjwQGSSAWORr1+/zo0bN6pN06pVK5TKu+vwREZGEh4eft9RVBcuXKB169YkJCTozccREhJCYGAgy5cvZ+3atbz99tt6v5RLS0uxsrLixx9/rLINv6ioiKKiu6u+5eTk4OHhQXZ2Nvb29nppb926RUpKCi1btjT4ZS40PFl5GdzMSafYAjQW4F5aioXWDsXNQl2aEmc77F3czXp1cK1Wi7+/P0OGDOHDDw0bDfh3iP+PZiL7MtGfvY/r14d0o6LShwWQbXuIec6OOOaCeyYM6/c2zwSNqevcCnUoJycHBweHSr+/yzOok7GLi4tu6OfD1rJlS9RqNdHR0boAJycnh6NHj+pGYgUFBZGVlUV8fLxuRMe+ffvQarV07969ynOrVCrd8FhBuJejXRNsrR0oLilAKUkoFDZgqaTYuYCSWwUorGywVtVsqL4pudOcFhISQlFREStXriQlJYXhw4fXddYEU+TQjD4zvuLKkCTSkhNQ+3XkkVYBkH2ZHlfj+dPSEg+3TqhtRc2NUHNG64Nz6dIlEhMTuXTpEhqNhsTERBITE3WTtAG0adNG1+9CJpMRHh7Ov/71L7Zu3UpSUhIjR47E3d1dN3uqv78/Tz75JK+99hrHjh0jLi6OyZMnM3ToUKONoBLqv48++khv+PO9n/79+9/3eIWFAlsrBxTWjrpaGqXKBluHJijrKLi5M8t0ZZ975y8yFrlcTmRkJF27diU4OJikpCT27t0r+soIRuXeKoBO/Ufi3ur2pKEOzVC3eYau3gNEcCMYzGjDxN9//32+/vpr3d/v9E/Yv3+/rn9AcnIy2dnZujTTpk0jPz+fcePGkZWVRc+ePdm1a5de1fS6deuYPHkyffr00U30t2LFCmPdhtAATJgwocIszHcYMny+Pvnyyy8pLCysdJ+Tk5PRr+/h4UFcXJzRryMIgmAsBvXBMRXVteGJNn9BqD/E/0dBEO5lSB+cejNMXBAEQRAE4WERAU4V7jcbqyAIxmeGFcyCIDwkRuuD01AplUrkcjlXrlzBxcUFpVJp8ORmgiD8fZIkcf36dWQymVhtXBAEg4kApxy5XE7Lli25evUqV65cqevsCIJZk8lkNG/eHAsLi7rOiiAIDYwIcCqhVCrx9PSktLS0xksXCILw8CkUChHcCILwQESAU4U71eKialwQBEEQGh7RyVgQBEEQBJMjAhxBEARBEEyOCHAEQRAEQTA5ZtkH587cGjk5OXWcE0EQBEEQaurO93ZN5sgyywAnNzcXKFtvRxAEQRCEhiU3NxcHB4dq05jlWlRarZYrV67QqFGjhz6JX05ODh4eHvz555/3XSfD3IiyqZ4on+qJ8qmeKJ+qibKpXkMqH0mSyM3Nxd3dHbm8+l42ZlmDI5fLad68uVGvYW9vX+8flLoiyqZ6onyqJ8qneqJ8qibKpnoNpXzuV3Nzh+hkLAiCIAiCyREBjiAIgiAIJkcEOA+ZSqVizpw5qFSqus5KvSPKpnqifKonyqd6onyqJsqmeqZaPmbZyVgQBEEQBNMmanAEQRAEQTA5IsARBEEQBMHkiABHEARBEASTIwIcQRAEQRBMjghwHsCqVavw8vLCysqK7t27c+zYsWrT//jjj7Rp0wYrKysCAgLYsWNHLeW09hlSNpGRkchkMr2PlZVVLea2dh04cICBAwfi7u6OTCZj8+bN9z0mJiaGTp06oVKp8Pb2JjIy0uj5rAuGlk1MTEyFZ0cmk5GWllY7Ga5lCxYsoGvXrjRq1IimTZsyePBgkpOT73ucubx7HqR8zOX989lnn9G+fXvdJH5BQUHs3Lmz2mNM5bkRAY6BNmzYwFtvvcWcOXM4ceIEHTp0ICwsjGvXrlWa/tChQwwbNoxXX32VhIQEBg8ezODBgzl16lQt59z4DC0bKJs58+rVq7pPampqLea4duXn59OhQwdWrVpVo/QpKSk89dRTPP744yQmJhIeHs7YsWPZvXu3kXNa+wwtmzuSk5P1np+mTZsaKYd1KzY2lkmTJnHkyBGioqIoKSnhiSeeID8/v8pjzOnd8yDlA+bx/mnevDkLFy4kPj6eX375hd69ezNo0CBOnz5daXqTem4kwSDdunWTJk2apPu7RqOR3N3dpQULFlSafsiQIdJTTz2lt6179+7S+PHjjZrPumBo2UREREgODg61lLv6BZA2bdpUbZpp06ZJ7dq109v20ksvSWFhYUbMWd2rSdns379fAqTMzMxayVN9c+3aNQmQYmNjq0xjTu+e8mpSPub8/mncuLH05ZdfVrrPlJ4bUYNjgOLiYuLj4+nbt69um1wup2/fvhw+fLjSYw4fPqyXHiAsLKzK9A3Vg5QNQF5eHi1atMDDw6PaXxXmyFyenb8jMDAQNzc3+vXrR1xcXF1np9ZkZ2cD4OTkVGUac35+alI+YH7vH41Gw/r168nPzycoKKjSNKb03IgAxwAZGRloNBpcXV31tru6ulbZ9p+WlmZQ+obqQcrGz8+PtWvXsmXLFr799lu0Wi09evTgr7/+qo0s13tVPTs5OTkUFhbWUa7qBzc3Nz7//HN++uknfvrpJzw8PAgNDeXEiRN1nTWj02q1hIeHExwczCOPPFJlOnN595RX0/Ixp/dPUlISdnZ2qFQqJkyYwKZNm2jbtm2laU3puTHL1cSF+iEoKEjvV0SPHj3w9/dn9erVfPjhh3WYM6G+8/Pzw8/PT/f3Hj16cP78eZYtW8Z///vfOsyZ8U2aNIlTp05x8ODBus5KvVTT8jGn94+fnx+JiYlkZ2ezceNGRo0aRWxsbJVBjqkQNTgGaNKkCRYWFqSnp+ttT09PR61WV3qMWq02KH1D9SBlU55CoaBjx46cO3fOGFlscKp6duzt7bG2tq6jXNVf3bp1M/lnZ/LkyWzbto39+/fTvHnzatOay7vnXoaUT3mm/P5RKpV4e3vTuXNnFixYQIcOHVi+fHmlaU3puREBjgGUSiWdO3cmOjpat02r1RIdHV1le2ZQUJBeeoCoqKgq0zdUD1I25Wk0GpKSknBzczNWNhsUc3l2HpbExESTfXYkSWLy5Mls2rSJffv20bJly/seY07Pz4OUT3nm9P7RarUUFRVVus+knpu67uXc0Kxfv15SqVRSZGSkdObMGWncuHGSo6OjlJaWJkmSJL388svSjBkzdOnj4uIkS0tLacmSJdLZs2elOXPmSAqFQkpKSqqrWzAaQ8tm3rx50u7du6Xz589L8fHx0tChQyUrKyvp9OnTdXULRpWbmyslJCRICQkJEiB9/PHHUkJCgpSamipJkiTNmDFDevnll3XpL1y4INnY2EjvvvuudPbsWWnVqlWShYWFtGvXrrq6BaMxtGyWLVsmbd68Wfrjjz+kpKQk6Y033pDkcrm0d+/euroFo5o4caLk4OAgxcTESFevXtV9CgoKdGnM+d3zIOVjLu+fGTNmSLGxsVJKSor066+/SjNmzJBkMpm0Z88eSZJM+7kRAc4D+PTTTyVPT09JqVRK3bp1k44cOaLbFxISIo0aNUov/Q8//CD5+vpKSqVSateunbR9+/ZaznHtMaRswsPDdWldXV2lAQMGSCdOnKiDXNeOO0Oby3/ulMmoUaOkkJCQCscEBgZKSqVSatWqlRQREVHr+a4NhpbNokWLpNatW0tWVlaSk5OTFBoaKu3bt69uMl8LKisbQO95MOd3z4OUj7m8f1555RWpRYsWklKplFxcXKQ+ffroghtJMu3nRiZJklR79UWCIAiCIAjGJ/rgCIIgCIJgckSAIwiCIAiCyREBjiAIgiAIJkcEOIIgCIIgmBwR4AiCIAiCYHJEgCMIgiAIgskRAY4gCIIgCCZHBDiCIAiCIJgcEeAIgiAIgmByRIAjCIIgCILJEQGOIAiCIAgmRwQ4giAIgiCYnP8HIruUGwcgy5UAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0, np.pi, n_theta)\n",
    "ref = f(t)\n",
    "plt.plot(t, ref, label=\"reference\")\n",
    "\n",
    "for quadrature in [legendre_gauss_weights, lobatto_weights, clenshaw_curtiss_weights]:\n",
    "    cost, wq = quadrature(n_theta, -1, 1)\n",
    "    tq = np.flip(np.arccos(cost))\n",
    "\n",
    "    if quadrature == lobatto_weights or quadrature == legendre_gauss_weights:\n",
    "        f_interp = interpolate(t, tq, ref)\n",
    "        mmax = len(tq)\n",
    "    else:\n",
    "        f_interp = ref\n",
    "        mmax = len(tq)\n",
    "\n",
    "    out = project(tq, wq, f_interp, mmax=mmax)\n",
    "\n",
    "    plt.plot(tq, out.numpy(), '.-', label=quadrature.__name__)\n",
    "\n",
    "plt.legend(loc='lower left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "again, let us plot the overall error, this time including the interpolation error:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(0, np.pi, n_theta)\n",
    "ref = f(t)\n",
    "\n",
    "fig, ax = plt.subplots(2, 1)\n",
    "\n",
    "for quadrature in [legendre_gauss_weights, lobatto_weights, clenshaw_curtiss_weights]:\n",
    "    cost, wq = quadrature(n_theta, -1, 1)\n",
    "    tq = np.flip(np.arccos(cost))\n",
    "\n",
    "    if quadrature == lobatto_weights or quadrature == legendre_gauss_weights:\n",
    "        f_interp = interpolate(t, tq, ref)\n",
    "        mmax = len(tq)\n",
    "    else:\n",
    "        f_interp = ref\n",
    "        mmax = len(tq)\n",
    "\n",
    "    out = project(tq, wq, f_interp, mmax=mmax)\n",
    "\n",
    "    ax[0].semilogy(tq, (out - f(tq)).numpy(), '.-', label=quadrature.__name__)\n",
    "    ax[1].semilogy(tq, (paddle.to_tensor(f_interp) - paddle.to_tensor(f(tq))).numpy(), '.-', label=quadrature.__name__)\n",
    "\n",
    "ax[0].set_title(\"Projection error after interpolation\")\n",
    "ax[1].set_title(\"Interpolation error\")\n",
    "# ax[0].legend(loc='lower left')\n",
    "# ax[1].legend(loc='lower left')\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can see that the interpolation dominates when we interpolate the solution. For this reason, it is reasonable t choose Clenshaw-Curtiss quadrature in scenarios where we expect the interpolation error to dominate."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.13"
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